Optimality and Duality of Approximate Quasi Weakly Efficient Solution for Nonsmooth Vector Optimization Problems

Abstract

This paper aims at studying optimality conditions and duality theorems of an approximate quasi weakly efficient solution for a class of nonsmooth vector optimization problems (VOP). First, a necessary optimality condition to the problem (VOP) is established by using the Clarke subdifferential. Second, the concept of approximate pseudo quasi type-I function is introduced, and under its hypothesis, a sufficient optimality condition to the problem (VOP) is also obtained. Finally, the approximate Mond–Weir dual model of the problem (VOP) is presented, and then, weak, strong, and converse duality theorems are established.

Local isolated efficiency in non-smooth robust semi-infinite multi-objective fractional programming problems

“…By taking into consideration some contributions from variational analysis and generalized differentiation such as Mordukhovich subdifferential [26] of an extended real-valued function, Choung [13] provided some new necessary and sufficient optimal conditions in a fuzzy form for an approximate weak Pareto solution of a cone constrained non-smooth non-convex vector optimization problem. Li and Yu [24] employed another tool of variational analysis, Clarke subdifferential, and established a necessary optimality condition for an approximate quasi-weakly efficient solution of a non-smooth vector optimization problem. They proposed a new type of generalized convexity named the approximate pseudo quasi type-I functions, and utilized it to study the sufficient optimality condition to the problem with respect to the concept of approximate quasi weakly efficiency.…”