Necessary and Suﬃcient Conditions for Weak Quasi Eﬃciency in Nonsmooth Multiobjective Problems. (3rd June 2017) - Golestani, M.; Sadeghi, H.; Tavan, Y.
ABSTRACT: In this article, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given and the relations between them are analyzed. We establish Kuhn-Tucker and strong Kuhn-Tucker necessary optimality conditions for (weak) quasi eﬃciency in terms of the Clarke subdifferential. By using two new classes of generalized convex functions, suﬃcient conditions for local (weak) quasi eﬃcient are also provided. Furthermore, we study the Mond-Weir type dual problem and establish weak, strong and converse duality results.