Duality gap in convex programming

Duality gap in convex programming

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Article ID: iaor20051094
Country: Germany
Volume: 99
Issue: 3
Start Page Number: 487
End Page Number: 498
Publication Date: Jan 2004
Journal: Mathematical Programming
Authors:
Keywords: duality
Abstract:

In this paper, we consider general convex programming problems and give a sufficient condition for the equality of the infimum of the original problem and the supremum of its ordinary dual. This condition may be seen as a continuity assumption on the constraint sets (i.e. on the sublevel sets of the constraint function) under linear perturbation. It allows us to generalize as well as treat previous results in a unified framework. Our main result is in fact based on a quite general constraint qualification result for quasiconvex programs involving a convex objective function proven in the setting of a real normed vector space.

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