# Convex optimization problem

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

Convex optimization minimizes a convex objective on a convex feasible domain; problem qualification, feasibility, evaluation and global optimality are distinct obligations.

mko-convex-optimization-problem · definition · v0.10.0



## Mathematical statement

A minimization problem qualifies here as convex only when its objective function and feasible domain are convex. This slice checks qualification for a univariate interval and quadratic objective, single-point feasibility, single-point evaluation and a comparison between two feasible candidates.





## Representative formula (exact TeX)

C(P)





## Assumptions


- The feasible domain is an explicit real interval and the objective is an integer-coefficient quadratic.
- Qualification or one-/two-point checks do not establish a global solution; KKT, general solvers and convergence results are not introduced.





## Symbol scope


- C — convex-problem qualification record
- f — objective function





## Intuition, definition, and misconceptions

Audit objective convexity and feasible-domain convexity separately.

Checking a feasible point and evaluating its objective are not optimality checks.

Comparing two candidates says only which has the lower value between them, not which is globally optimal.

Do not infer a unique global solution merely from the word convex or call the better of two candidates optimal for the whole problem.





## Adopted derivation guide

[Convex optimization problem: qualification, feasibility, single-point evaluation and a two-candidate comparison, and what they do not imply](https://ocme.evemisslab.com/en/derivations/derivation-mko-convex-optimization-problem-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites


- [Convex function](https://ocme.evemisslab.com/en/mko/mko-convex-function/) — Objective convexity is one convex-optimization qualification.
- [Optimization problem](https://ocme.evemisslab.com/en/mko/mko-optimization-problem/) — General optimization supplies feasible-domain, objective and minimization semantics.
- [Real vector space](https://ocme.evemisslab.com/en/mko/mko-real-vector-space/) — The feasible domain lies in a real vector space.





## Verification boundary

Only problem qualification, feasibility, evaluation and two-point comparison are handled; a solved optimization problem is not claimed.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.





## Next obligation

Add optimality certificates, KKT, duality and algorithmic convergence.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/convex-optimization-problem.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-convex-optimization-problem/index.md)