Existence of optimal solutions and duality results under weak conditions

Existence of optimal solutions and duality results under weak conditions

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Article ID: iaor20013608
Country: Germany
Volume: 88
Issue: 1
Start Page Number: 45
End Page Number: 59
Publication Date: Jan 2000
Journal: Mathematical Programming
Authors:
Keywords: duality
Abstract:

In this paper we consider an ordinary convex program with no qualification conditions (such as Slater's condition) and for which the optimal set is neither required to be compact, nor to be equal to the sum of a compact set and a linear space. It is supposed only that the infimum α is finite. A very wide class of convex functions is exhibited for which the optimum is always attained and α is equal to the supremum of the ordinary dual program. Additional results concerning the existence of optimal solutions in the non convex case are also given.

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