In this paper, we study the nonconvex nonsmooth optimization problem (P) of minimizing a tangentially convex function with inequality constraints where constraint functions are convex. This is done by using cone tangential subdifferentials together new qualification. Indeed, present qualification to guarantee that Karush-Kuhn-Tucker conditions necessary and sufficient for optimality (P). Moreov...

This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a secondorder generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues rela...

In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results ar...

This is an expository article whose main aim is to introduce nor~nal affine semigroups and its links with other areas such as graph tlleory, linear programming and polyhedral geometry. As an application we derive the classical and generalized ~narriage theorems. 1 Introduction Let A = (a i j) be an integral matrix of order n x q with nonzero distinct columns and let A = {vl,. .. ,v,) be the set...

In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.

In this paper, we first introduce a generalized concept of Berge strong equilibrium for a generalized game G = (Xi; Ti, fi)i∈I of normal form, and using a fixed point theorem for compact acyclic maps in admissible convex sets, we establish the existence theorem of generalized Berge strong equilibrium for the game G with acyclic values. Also, we have demonstrated by examples that our new approac...