Sucient Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems via Higher-Order Strong Convexity

Abstract

In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdierential. Suitable examples illustrating the nonemptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided. These generalizations are then employed to establish sucient optimality conditions for a nonsmooth multiobjective optimization problem involving support functions of compact convex sets. Furthermore, we formulate a mixed type dual model for the primal problem and establish weak and strong duality theorems using the notion of strict eciency of order m. The results presented in this paper extend and unify several known results from the literature to a more general class of functions as well as optimization problems.
Keywords: Nonsmooth multiobjective programming; Support functions; Strict minimizers; Optimality conditions; Mixed duality.