# Concept derivation guides

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Concept guide



## [Convex optimization problem: qualification, feasibility, single-point evaluation and a two-candidate comparison, and what they do not imply](/en/derivations/derivation-mko-convex-optimization-problem-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-convex-optimization-problem)

Problem P: minimize f(x)=x²−6x+10 over the feasible domain X=[0,5]. (1) Check separately that the domain and the objective are convex, so that P qualifies as a convex problem; (2) decide feasibility of the candidates x₁=1, x₂=4, x₃=−1; (3) evaluate f(1) and f(4) and compare the two feasible candidates; (4) explain why the candidate with the lower objective value is not thereby an optimal solution of P, and use P′: minimize x² over X′=(0,1], to show that a convex problem need not have a minimizer.

Convex optimization problem

derivation-mko-convex-optimization-problem-01





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