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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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Authors and Affiliations

  1. Laboratoire d’Analyse Non Linéaire Appliquée, U.F.R. des Sciences et Techniques, Université de Toulon et du Var, Avenue de l’Université, BP 132, 83957, La Garde Cedex, France

    T. Champion

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  1. T. Champion
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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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