Duality for Anticonvex Programs |
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Authors: | Jean-Paul Penot |
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Institution: | (1) Département de Mathématiques, Laboratoire de Mathématiques Appliquées, CNRS UPRES A 5033, Faculté des Sciences, Av. de l'Université, F-64000 Pau, France |
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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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Keywords: | Conjugacy Duality Even convexity Nonconvex duality Polar set Quasiconvex function Radiant set Reverse convex program Shady set |
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