Quasi Efficient Solutions and Duality Results in a Multiobjective Optimization Problem with Mixed Constraints via Tangential Subdifferentials

Abstract

We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing a suitable constraint qualification, we formulate both necessary and sufficient optimality conditions for (local) quasi efficient solutions in terms of tangential subdifferentials. Furthermore, under generalized convexity assumptions, we state strong, weak and converse duality relations of Wolfe and Mond–Weir types. We give a number of examples to illustrate the new concepts and main results of this paper.

Keywords

• nonlinear programming
• optimality conditions
• quasi efficient solutions
• tangential subdifferential
• Wolfe and Mond–Weir duality