Optimality and Duality Theorems in Nonsmooth Multiobjective Optimization

Abstract

In this paper, we consider a class of nonsmooth multiobjective programming problems. Necessary and sufficient optimality conditions are obtained under higher order strongly convexity for Lipschitz functions. We formulate Mond-Weir type dual problem and establish weak and strong duality theorems for a strict minimizer of order m.

Sufficient optimality conditions and duality for nonsmooth multiobjective optimization problems via higher order strong convexity

“…It is evident by the definitions that every efficient minimizer of order m for (NMOP) is also strict minimizer of order m. Now, we state the following necessary optimality conditions for (NMOP) established by Bae and Kim [4].…”

“…Motivated by Chandra et al [7], Bae and Kim [4] introduced the following regularity conditions for (NMOP) Definition 3.1. Let x 0 be a feasible solution for (NMOP).…”

“…Bae and Kim [4] obtained necessary and sufficient optimality conditions for a nonsmooth optimization problem under higher order strong convexity assumptions and established weak and strong duality theorems for a strict minimizer of order m. Recently, Arora et al [1] have introduced four new generalized classes of strongly convex functions of order m and derived the characterizations of the solution sets of strict minimizers of order m. They have also established sufficient optimality conditions for a multiobjective optimization problem and obtained mixed duality results.…”

“…Motivated by [1,[4][5], we consider a class of nonsmooth multiobjective optimization problem involving support functions of compact convex sets and derive sufficient optimality conditions for efficient minimizers of order m in the framework of some new generalizations of strong convexity of order m. Related to the primal problem, we formulate a mixed dual model and establish weak and strong duality theorems.…”

Optimality and duality for nonsmooth semi-infinite multiobjective programming with support functions

“…Many authors have formulated Mond-Weir type dual and established duality results in various optimization problems with support functions; see [1,2,13,21,22,30] and the references therein. Following the above mentioned works, we formulate Mond-Weir type dual for nonsmooth semi-infinite programming problem with support function (MOSIP) and establish duality theorems.…”