# 最佳化密度：有限local/global與證書邊界基礎 · 脈衝 R07

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261119-r07-optimization-problem-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[1,2,3,4]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 1], [B, 2], [C, 3], [D, 4]], [[A, B], [A, C], [B, D], [C, D]], A, 1, [[B, 2], [C, 3]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 1], [B, 2], [C, 3], [D, 4]], [[A, B], [A, C], [B, D], [C, D]], A, 1, [[B, 2], [C, 3]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0001/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 2. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[2,4,6,8]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 2], [B, 4], [C, 6], [D, 8]], [[A, B], [A, C], [B, D], [C, D]], A, 2, [[B, 4], [C, 6]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 2], [B, 4], [C, 6], [D, 8]], [[A, B], [A, C], [B, D], [C, D]], A, 2, [[B, 4], [C, 6]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0002/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 3. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[3,6,9,12]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 3], [B, 6], [C, 9], [D, 12]], [[A, B], [A, C], [B, D], [C, D]], A, 3, [[B, 6], [C, 9]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 3], [B, 6], [C, 9], [D, 12]], [[A, B], [A, C], [B, D], [C, D]], A, 3, [[B, 6], [C, 9]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0003/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 4. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[4,8,12,16]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 4], [B, 8], [C, 12], [D, 16]], [[A, B], [A, C], [B, D], [C, D]], A, 4, [[B, 8], [C, 12]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 4], [B, 8], [C, 12], [D, 16]], [[A, B], [A, C], [B, D], [C, D]], A, 4, [[B, 8], [C, 12]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0004/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 5. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[5,10,15,20]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 5], [B, 10], [C, 15], [D, 20]], [[A, B], [A, C], [B, D], [C, D]], A, 5, [[B, 10], [C, 15]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 5], [B, 10], [C, 15], [D, 20]], [[A, B], [A, C], [B, D], [C, D]], A, 5, [[B, 10], [C, 15]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0005/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 6. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[6,12,18,24]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 6], [B, 12], [C, 18], [D, 24]], [[A, B], [A, C], [B, D], [C, D]], A, 6, [[B, 12], [C, 18]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 6], [B, 12], [C, 18], [D, 24]], [[A, B], [A, C], [B, D], [C, D]], A, 6, [[B, 12], [C, 18]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0006/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 7. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[7,14,21,28]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 7], [B, 14], [C, 21], [D, 28]], [[A, B], [A, C], [B, D], [C, D]], A, 7, [[B, 14], [C, 21]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 7], [B, 14], [C, 21], [D, 28]], [[A, B], [A, C], [B, D], [C, D]], A, 7, [[B, 14], [C, 21]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0007/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 8. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[8,16,24,32]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 8], [B, 16], [C, 24], [D, 32]], [[A, B], [A, C], [B, D], [C, D]], A, 8, [[B, 16], [C, 24]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 8], [B, 16], [C, 24], [D, 32]], [[A, B], [A, C], [B, D], [C, D]], A, 8, [[B, 16], [C, 24]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0008/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 9. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[9,18,27,36]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 9], [B, 18], [C, 27], [D, 36]], [[A, B], [A, C], [B, D], [C, D]], A, 9, [[B, 18], [C, 27]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 9], [B, 18], [C, 27], [D, 36]], [[A, B], [A, C], [B, D], [C, D]], A, 9, [[B, 18], [C, 27]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0009/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 10. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[10,20,30,40]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 10], [B, 20], [C, 30], [D, 40]], [[A, B], [A, C], [B, D], [C, D]], A, 10, [[B, 20], [C, 30]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 10], [B, 20], [C, 30], [D, 40]], [[A, B], [A, C], [B, D], [C, D]], A, 10, [[B, 20], [C, 30]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0010/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 11. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[11,22,33,44]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 11], [B, 22], [C, 33], [D, 44]], [[A, B], [A, C], [B, D], [C, D]], A, 11, [[B, 22], [C, 33]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 11], [B, 22], [C, 33], [D, 44]], [[A, B], [A, C], [B, D], [C, D]], A, 11, [[B, 22], [C, 33]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0011/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 12. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[12,24,36,48]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 12], [B, 24], [C, 36], [D, 48]], [[A, B], [A, C], [B, D], [C, D]], A, 12, [[B, 24], [C, 36]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 12], [B, 24], [C, 36], [D, 48]], [[A, B], [A, C], [B, D], [C, D]], A, 12, [[B, 24], [C, 36]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0012/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 13. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[13,26,39,52]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 13], [B, 26], [C, 39], [D, 52]], [[A, B], [A, C], [B, D], [C, D]], A, 13, [[B, 26], [C, 39]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 13], [B, 26], [C, 39], [D, 52]], [[A, B], [A, C], [B, D], [C, D]], A, 13, [[B, 26], [C, 39]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0013/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 14. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[14,28,42,56]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 14], [B, 28], [C, 42], [D, 56]], [[A, B], [A, C], [B, D], [C, D]], A, 14, [[B, 28], [C, 42]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 14], [B, 28], [C, 42], [D, 56]], [[A, B], [A, C], [B, D], [C, D]], A, 14, [[B, 28], [C, 42]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0014/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 15. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[15,30,45,60]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 15], [B, 30], [C, 45], [D, 60]], [[A, B], [A, C], [B, D], [C, D]], A, 15, [[B, 30], [C, 45]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 15], [B, 30], [C, 45], [D, 60]], [[A, B], [A, C], [B, D], [C, D]], A, 15, [[B, 30], [C, 45]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0015/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 16. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[16,32,48,64]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 16], [B, 32], [C, 48], [D, 64]], [[A, B], [A, C], [B, D], [C, D]], A, 16, [[B, 32], [C, 48]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 16], [B, 32], [C, 48], [D, 64]], [[A, B], [A, C], [B, D], [C, D]], A, 16, [[B, 32], [C, 48]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0016/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 17. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[17,34,51,68]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 17], [B, 34], [C, 51], [D, 68]], [[A, B], [A, C], [B, D], [C, D]], A, 17, [[B, 34], [C, 51]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 17], [B, 34], [C, 51], [D, 68]], [[A, B], [A, C], [B, D], [C, D]], A, 17, [[B, 34], [C, 51]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0017/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 18. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[18,36,54,72]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 18], [B, 36], [C, 54], [D, 72]], [[A, B], [A, C], [B, D], [C, D]], A, 18, [[B, 36], [C, 54]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 18], [B, 36], [C, 54], [D, 72]], [[A, B], [A, C], [B, D], [C, D]], A, 18, [[B, 36], [C, 54]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0018/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 19. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[19,38,57,76]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 19], [B, 38], [C, 57], [D, 76]], [[A, B], [A, C], [B, D], [C, D]], A, 19, [[B, 38], [C, 57]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 19], [B, 38], [C, 57], [D, 76]], [[A, B], [A, C], [B, D], [C, D]], A, 19, [[B, 38], [C, 57]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0019/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 20. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[20,40,60,80]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 20], [B, 40], [C, 60], [D, 80]], [[A, B], [A, C], [B, D], [C, D]], A, 20, [[B, 40], [C, 60]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 20], [B, 40], [C, 60], [D, 80]], [[A, B], [A, C], [B, D], [C, D]], A, 20, [[B, 40], [C, 60]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0020/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 21. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[21,42,63,84]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 21], [B, 42], [C, 63], [D, 84]], [[A, B], [A, C], [B, D], [C, D]], A, 21, [[B, 42], [C, 63]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 21], [B, 42], [C, 63], [D, 84]], [[A, B], [A, C], [B, D], [C, D]], A, 21, [[B, 42], [C, 63]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0021/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 22. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[22,44,66,88]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 22], [B, 44], [C, 66], [D, 88]], [[A, B], [A, C], [B, D], [C, D]], A, 22, [[B, 44], [C, 66]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 22], [B, 44], [C, 66], [D, 88]], [[A, B], [A, C], [B, D], [C, D]], A, 22, [[B, 44], [C, 66]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0022/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 23. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[23,46,69,92]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 23], [B, 46], [C, 69], [D, 92]], [[A, B], [A, C], [B, D], [C, D]], A, 23, [[B, 46], [C, 69]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 23], [B, 46], [C, 69], [D, 92]], [[A, B], [A, C], [B, D], [C, D]], A, 23, [[B, 46], [C, 69]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0023/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 24. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[24,48,72,96]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 24], [B, 48], [C, 72], [D, 96]], [[A, B], [A, C], [B, D], [C, D]], A, 24, [[B, 48], [C, 72]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 24], [B, 48], [C, 72], [D, 96]], [[A, B], [A, C], [B, D], [C, D]], A, 24, [[B, 48], [C, 72]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0024/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 25. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[25,50,75,100]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。

local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。

查看答案與解釋([[A, 25], [B, 50], [C, 75], [D, 100]], [[A, B], [A, C], [B, D], [C, D]], A, 25, [[B, 50], [C, 75]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)

Wave6第十三層核對=([[A, 25], [B, 50], [C, 75], [D, 100]], [[A, B], [A, C], [B, D], [C, D]], A, 25, [[B, 50], [C, 75]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0025/)

最佳化問題 · qf-mod50-optdeep-local-global · candidate





## 26. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[3,1,4,5]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 3], [B, 1], [C, 4], [D, 5]], A, 3, B, 1, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 3], [B, 1], [C, 4], [D, 5]], A, 3, B, 1, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0026/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 27. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[6,2,8,10]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 6], [B, 2], [C, 8], [D, 10]], A, 6, B, 2, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 6], [B, 2], [C, 8], [D, 10]], A, 6, B, 2, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0027/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 28. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[9,3,12,15]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 9], [B, 3], [C, 12], [D, 15]], A, 9, B, 3, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 9], [B, 3], [C, 12], [D, 15]], A, 9, B, 3, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0028/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 29. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[12,4,16,20]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 12], [B, 4], [C, 16], [D, 20]], A, 12, B, 4, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 12], [B, 4], [C, 16], [D, 20]], A, 12, B, 4, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0029/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 30. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[15,5,20,25]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 15], [B, 5], [C, 20], [D, 25]], A, 15, B, 5, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 15], [B, 5], [C, 20], [D, 25]], A, 15, B, 5, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0030/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 31. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[18,6,24,30]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 18], [B, 6], [C, 24], [D, 30]], A, 18, B, 6, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 18], [B, 6], [C, 24], [D, 30]], A, 18, B, 6, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0031/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 32. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[21,7,28,35]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 21], [B, 7], [C, 28], [D, 35]], A, 21, B, 7, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 21], [B, 7], [C, 28], [D, 35]], A, 21, B, 7, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0032/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 33. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[24,8,32,40]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 24], [B, 8], [C, 32], [D, 40]], A, 24, B, 8, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 24], [B, 8], [C, 32], [D, 40]], A, 24, B, 8, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0033/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 34. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[27,9,36,45]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 27], [B, 9], [C, 36], [D, 45]], A, 27, B, 9, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 27], [B, 9], [C, 36], [D, 45]], A, 27, B, 9, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0034/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 35. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[30,10,40,50]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 30], [B, 10], [C, 40], [D, 50]], A, 30, B, 10, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 30], [B, 10], [C, 40], [D, 50]], A, 30, B, 10, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0035/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 36. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[33,11,44,55]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 33], [B, 11], [C, 44], [D, 55]], A, 33, B, 11, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 33], [B, 11], [C, 44], [D, 55]], A, 33, B, 11, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0036/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 37. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[36,12,48,60]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 36], [B, 12], [C, 48], [D, 60]], A, 36, B, 12, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 36], [B, 12], [C, 48], [D, 60]], A, 36, B, 12, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0037/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 38. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[39,13,52,65]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 39], [B, 13], [C, 52], [D, 65]], A, 39, B, 13, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 39], [B, 13], [C, 52], [D, 65]], A, 39, B, 13, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0038/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 39. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[42,14,56,70]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 42], [B, 14], [C, 56], [D, 70]], A, 42, B, 14, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 42], [B, 14], [C, 56], [D, 70]], A, 42, B, 14, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0039/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 40. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[45,15,60,75]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 45], [B, 15], [C, 60], [D, 75]], A, 45, B, 15, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 45], [B, 15], [C, 60], [D, 75]], A, 45, B, 15, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0040/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 41. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[48,16,64,80]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 48], [B, 16], [C, 64], [D, 80]], A, 48, B, 16, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 48], [B, 16], [C, 64], [D, 80]], A, 48, B, 16, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0041/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 42. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[51,17,68,85]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 51], [B, 17], [C, 68], [D, 85]], A, 51, B, 17, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 51], [B, 17], [C, 68], [D, 85]], A, 51, B, 17, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0042/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 43. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[54,18,72,90]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 54], [B, 18], [C, 72], [D, 90]], A, 54, B, 18, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 54], [B, 18], [C, 72], [D, 90]], A, 54, B, 18, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0043/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 44. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[57,19,76,95]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 57], [B, 19], [C, 76], [D, 95]], A, 57, B, 19, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 57], [B, 19], [C, 76], [D, 95]], A, 57, B, 19, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0044/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 45. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[60,20,80,100]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 60], [B, 20], [C, 80], [D, 100]], A, 60, B, 20, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 60], [B, 20], [C, 80], [D, 100]], A, 60, B, 20, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0045/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 46. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[63,21,84,105]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 63], [B, 21], [C, 84], [D, 105]], A, 63, B, 21, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 63], [B, 21], [C, 84], [D, 105]], A, 63, B, 21, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0046/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 47. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[66,22,88,110]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 66], [B, 22], [C, 88], [D, 110]], A, 66, B, 22, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 66], [B, 22], [C, 88], [D, 110]], A, 66, B, 22, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0047/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 48. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[69,23,92,115]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 69], [B, 23], [C, 92], [D, 115]], A, 69, B, 23, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 69], [B, 23], [C, 92], [D, 115]], A, 69, B, 23, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0048/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 49. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[72,24,96,120]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 72], [B, 24], [C, 96], [D, 120]], A, 72, B, 24, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 72], [B, 24], [C, 96], [D, 120]], A, 72, B, 24, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0049/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 50. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[75,25,100,125]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。

查看答案與解釋([[A, 75], [B, 25], [C, 100], [D, 125]], A, 75, B, 25, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)

Wave6第十三層核對=([[A, 75], [B, 25], [C, 100], [D, 125]], A, 75, B, 25, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0050/)

最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate





## 51. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":1,"points":["A","B","C","D"],"values":[1,2,3,4]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 1], [B, 2], [C, 3], [D, 4]], 1, A, 1, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 1], [B, 2], [C, 3], [D, 4]], 1, A, 1, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0051/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 52. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":2,"points":["A","B","C","D"],"values":[2,4,6,8]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 2], [B, 4], [C, 6], [D, 8]], 2, A, 2, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 2], [B, 4], [C, 6], [D, 8]], 2, A, 2, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0052/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 53. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":3,"points":["A","B","C","D"],"values":[3,6,9,12]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 3], [B, 6], [C, 9], [D, 12]], 3, A, 3, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 3], [B, 6], [C, 9], [D, 12]], 3, A, 3, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0053/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 54. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":4,"points":["A","B","C","D"],"values":[4,8,12,16]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 4], [B, 8], [C, 12], [D, 16]], 4, A, 4, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 4], [B, 8], [C, 12], [D, 16]], 4, A, 4, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0054/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 55. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":5,"points":["A","B","C","D"],"values":[5,10,15,20]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 5], [B, 10], [C, 15], [D, 20]], 5, A, 5, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 5], [B, 10], [C, 15], [D, 20]], 5, A, 5, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0055/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 56. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":6,"points":["A","B","C","D"],"values":[6,12,18,24]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 6], [B, 12], [C, 18], [D, 24]], 6, A, 6, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 6], [B, 12], [C, 18], [D, 24]], 6, A, 6, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0056/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 57. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":7,"points":["A","B","C","D"],"values":[7,14,21,28]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 7], [B, 14], [C, 21], [D, 28]], 7, A, 7, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 7], [B, 14], [C, 21], [D, 28]], 7, A, 7, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0057/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 58. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":8,"points":["A","B","C","D"],"values":[8,16,24,32]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 8], [B, 16], [C, 24], [D, 32]], 8, A, 8, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 8], [B, 16], [C, 24], [D, 32]], 8, A, 8, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0058/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 59. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":9,"points":["A","B","C","D"],"values":[9,18,27,36]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 9], [B, 18], [C, 27], [D, 36]], 9, A, 9, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 9], [B, 18], [C, 27], [D, 36]], 9, A, 9, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0059/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 60. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":10,"points":["A","B","C","D"],"values":[10,20,30,40]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 10], [B, 20], [C, 30], [D, 40]], 10, A, 10, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 10], [B, 20], [C, 30], [D, 40]], 10, A, 10, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0060/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 61. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":11,"points":["A","B","C","D"],"values":[11,22,33,44]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 11], [B, 22], [C, 33], [D, 44]], 11, A, 11, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 11], [B, 22], [C, 33], [D, 44]], 11, A, 11, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0061/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 62. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":12,"points":["A","B","C","D"],"values":[12,24,36,48]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 12], [B, 24], [C, 36], [D, 48]], 12, A, 12, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 12], [B, 24], [C, 36], [D, 48]], 12, A, 12, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0062/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 63. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":13,"points":["A","B","C","D"],"values":[13,26,39,52]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 13], [B, 26], [C, 39], [D, 52]], 13, A, 13, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 13], [B, 26], [C, 39], [D, 52]], 13, A, 13, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0063/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 64. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":14,"points":["A","B","C","D"],"values":[14,28,42,56]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 14], [B, 28], [C, 42], [D, 56]], 14, A, 14, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 14], [B, 28], [C, 42], [D, 56]], 14, A, 14, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0064/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 65. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":15,"points":["A","B","C","D"],"values":[15,30,45,60]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 15], [B, 30], [C, 45], [D, 60]], 15, A, 15, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 15], [B, 30], [C, 45], [D, 60]], 15, A, 15, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0065/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 66. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":16,"points":["A","B","C","D"],"values":[16,32,48,64]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 16], [B, 32], [C, 48], [D, 64]], 16, A, 16, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 16], [B, 32], [C, 48], [D, 64]], 16, A, 16, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0066/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 67. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":17,"points":["A","B","C","D"],"values":[17,34,51,68]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 17], [B, 34], [C, 51], [D, 68]], 17, A, 17, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 17], [B, 34], [C, 51], [D, 68]], 17, A, 17, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0067/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 68. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":18,"points":["A","B","C","D"],"values":[18,36,54,72]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 18], [B, 36], [C, 54], [D, 72]], 18, A, 18, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 18], [B, 36], [C, 54], [D, 72]], 18, A, 18, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0068/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 69. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":19,"points":["A","B","C","D"],"values":[19,38,57,76]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 19], [B, 38], [C, 57], [D, 76]], 19, A, 19, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 19], [B, 38], [C, 57], [D, 76]], 19, A, 19, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0069/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 70. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":20,"points":["A","B","C","D"],"values":[20,40,60,80]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 20], [B, 40], [C, 60], [D, 80]], 20, A, 20, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 20], [B, 40], [C, 60], [D, 80]], 20, A, 20, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0070/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 71. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":21,"points":["A","B","C","D"],"values":[21,42,63,84]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 21], [B, 42], [C, 63], [D, 84]], 21, A, 21, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 21], [B, 42], [C, 63], [D, 84]], 21, A, 21, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0071/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 72. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":22,"points":["A","B","C","D"],"values":[22,44,66,88]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 22], [B, 44], [C, 66], [D, 88]], 22, A, 22, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 22], [B, 44], [C, 66], [D, 88]], 22, A, 22, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0072/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 73. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":23,"points":["A","B","C","D"],"values":[23,46,69,92]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 23], [B, 46], [C, 69], [D, 92]], 23, A, 23, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 23], [B, 46], [C, 69], [D, 92]], 23, A, 23, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0073/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 74. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":24,"points":["A","B","C","D"],"values":[24,48,72,96]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 24], [B, 48], [C, 72], [D, 96]], 24, A, 24, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 24], [B, 48], [C, 72], [D, 96]], 24, A, 24, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0074/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 75. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":25,"points":["A","B","C","D"],"values":[25,50,75,100]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。

查看答案與解釋([[A, 25], [B, 50], [C, 75], [D, 100]], 25, A, 25, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)

Wave6第十三層核對=([[A, 25], [B, 50], [C, 75], [D, 100]], 25, A, 25, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0075/)

最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate





## 76. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"empty_feasible","model":{}}；請依 [mode, feasible_set, optimizer_exists_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(empty_feasible, [], 否, empty_feasible_set_has_no_optimizer)

Wave6第十三層核對=(empty_feasible, [], 否, empty_feasible_set_has_no_optimizer)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0076/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 77. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[2,4]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 2], [B, 4]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 2], [B, 4]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0077/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 78. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[3,3,9]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 3, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 3, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0078/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 79. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[8,12,4,16]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 8, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 8, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0079/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 80. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[5,10]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 5], [B, 10]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 5], [B, 10]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0080/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 81. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[6,6,18]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 6, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 6, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0081/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 82. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[14,21,7,28]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 14, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 14, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0082/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 83. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[8,16]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 8], [B, 16]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 8], [B, 16]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0083/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 84. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[9,9,27]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 9, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 9, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0084/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 85. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[20,30,10,40]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 20, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 20, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0085/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 86. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[11,22]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 11], [B, 22]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 11], [B, 22]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0086/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 87. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[12,12,36]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 12, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 12, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0087/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 88. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[26,39,13,52]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 26, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 26, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0088/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 89. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[14,28]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 14], [B, 28]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 14], [B, 28]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0089/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 90. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[15,15,45]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 15, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 15, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0090/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 91. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[32,48,16,64]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 32, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 32, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0091/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 92. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[17,34]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 17], [B, 34]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 17], [B, 34]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0092/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 93. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[18,18,54]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 18, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 18, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0093/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 94. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[38,57,19,76]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 38, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 38, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0094/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 95. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[20,40]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 20], [B, 40]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 20], [B, 40]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0095/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 96. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[21,21,63]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 21, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 21, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0096/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 97. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[44,66,22,88]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 44, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 44, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0097/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 98. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[23,46]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(incomplete_domain, [[A, 23], [B, 46]], 否, an_unverified_partial_list_cannot_support_a_global_claim)

Wave6第十三層核對=(incomplete_domain, [[A, 23], [B, 46]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0098/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 99. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[24,24,72]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(tie_not_unique, 24, [A, B], 是, 否, global_optimum_need_not_be_unique)

Wave6第十三層核對=(tie_not_unique, 24, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0099/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate





## 100. 有限最佳化

完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[50,75,25,100]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。

四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。

查看答案與解釋(local_not_global, A, 50, [B], 是, 否, local_minimum_does_not_imply_global_minimum)

Wave6第十三層核對=(local_not_global, A, 50, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-pulse-20261119-r07-0100/)

最佳化問題 · qf-mod50-optdeep-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261119-r07-optimization-problem-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261119-r07-optimization-problem-foundations/validation-report.json)