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Article Dans Une Revue Optimization Letters Année : 2010

On representations of the feasible set in convex optimization

Résumé

We consider the convex optimization problem $\min \{ f(x) : g_j(x)\leq 0,\,j=1,\ldots,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.
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Dates et versions

hal-00430141 , version 1 (05-11-2009)

Identifiants

Citer

Jean-Bernard Lasserre. On representations of the feasible set in convex optimization. Optimization Letters, 2010, 4 (1), p. 1-5. ⟨10.1007/s11590-009-0153-6⟩. ⟨hal-00430141⟩
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