Conjugaison par tranches et dualitë de toland

Abstract

A level set duality scheme analoguous to Toland's one is developed. In particular, his formula on the difference of two functions finds its level-set analogue. In this way, new couples of dual optimization problems are obtained. Applications to the maximization of functions which level sets are P-closed (where Pis a not necessarily topological closure) are shown.

Keywords:

• Generalized Fenchel conjugation
• level sets
• quasi-convexity
• Toland's duality

AMS 1980 Subject Classification:

• Primary:49 A 55