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Duality gap in convex programming

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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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Correspondence to T. Champion.

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Mathematics Subject Classification (2000):90C25, 90C26, 90C30, 90C31

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Champion, T. Duality gap in convex programming. Math. Program., Ser. A 99, 487–498 (2004). https://doi.org/10.1007/s10107-003-0461-z

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  • DOI: https://doi.org/10.1007/s10107-003-0461-z

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