Generalized convex functions and generalized differentials

Thi Hong Linh Nguyen (1) , Jean-Paul Penot (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We study some classes of generalized convex functions, using a generalized differential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdifferential or a pseudo-differential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced. We devise some optimality conditions for constrained optimization problems. In particular, we get Lagrange-Kuhn-Tucker multipliers for mathematical programming problems.

Mots clés: colinvex; generalized differential; mathematical programming; optimality conditions; protoconvex function; pseudoconvex function; quasiconvex function.; quasiconvex function

Domaines: Optimisation et contrôle [math.OC]

Thi Hong Linh Nguyen, Jean-Paul Penot. Generalized convex functions and generalized differentials. 2006. ⟨hal-00423367⟩