Etudiant : EL FAYK ISMAIL

Filière : Master Mathématiques Appliquées et Systèmes Intelligents (MASI)

Encadrant : Pr. GADHI NAZIH ABDERRAZZAK

Annèe : 2026

Résumé : The purpose of this thesis is to develop optimality conditions and duality theory for a constrained nonsmooth minimax programming problem in which the objective and constraint functions are not necessarily differentiable. To this end, two generalized subdifferentials, which are more suitable to this structure than the classical gradient, are employed. These are the convexificator proposed by Demyanov and the tangential subdifferential proposed by Pshenichnyi. Necessary optimality conditions of Karush–Kuhn–Tucker type are derived in terms of convexificators and the tangential subdifferential and shown to be sufficient under generalized convexity assumptions such as pseudoconvexity and quasiconvexity. Under these conditions, dual problems of Mond-Weir and Wolfe type are formulated for the two subdifferentials and weak, strong and strict converse duality are proved in each case.