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Duality for Anticonvex Programs

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Abstract

Calling anticonvex a program which is either a maximization of a convex function on a convex set or a minimization of a convex function on the set of points outside a convex subset, we introduce several dual problems related to each of these problems. We give conditions ensuring there is no duality gap. We show how solutions to the dual problems can serve to locate solutions of the primal problem.

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  1. Département de Mathématiques, Laboratoire de Mathématiques Appliquées, CNRS UPRES A 5033, Faculté des Sciences, Av. de l'Université, F-64000, Pau, France

    Jean-Paul Penot

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Penot, JP. Duality for Anticonvex Programs. Journal of Global Optimization 19, 163–182 (2001). https://doi.org/10.1023/A:1008327614099

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