OPTIMALITY CONDITIONS AND DUALITY FOR APPROXIMATE SOLUTIONS OF VECTOR OPTIMIZATION PROBLEMS

In this paper, we study approximate solutions of vector optimization problems. We introduce the concept of cone convex functions with respect to (in short w.r.t.) a mapping. Under this kind of cone convexity assumption, we obtain the Karush-Kuhn-Tucker type necessary and sufficient optimality conditions for quasiminimal solutions w.r.t. a mapping of vector optimization problems. We formulate approximate Mond-Weir type dual problem and establish the duality results. We also consider vector optimization problems with perturbed cone constraint. The necessary and sufficient optimality conditions and duality results for quasi-solutions w.r.t. a mapping of vector optimization problems with perturbed cone constraint are established.