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

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.