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Journal of Convex Analysis 23 (2016), No. 2, 615--629
Copyright Heldermann Verlag 2016

Zero Duality Gap and Attainment with Possibly Non-Convex Data

Emil Ernst
Université Aix Marseille, Centrale Marseille, I2M -- UMR 7373, 13453 Marseille, France

Michel Volle
Université d'Avignon, 74 rue Louis Pasteur, 84029 Avignon Cedex 1, France

A newly defined notion of convex closedness regarding a set is used in order to state a necessary and sufficient criterion for the min-sup property in non necessarily convex primal-dual optimization problems, generalizing well-known theorems valid in the convex setting. Our main result is then applied to the classical penalty method.

Keywords: Dual optimization, min-sup property, convex closedness regarding a set, penalty method.

MSC: 49M30, 49N15, 52A20

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