SCALARIZATIONS AND LAGRANGE MULTIPLIERS FOR APPROXIMATE SOLUTIONS IN THE VECTOR OPTIMIZATION PROBLEMS WITH SET-VALUED MAPS

In this paper, we characterize approximate solutions of vector optimization problems with set-valued maps. We gives several characterizations of generalized subconvexlike set-valued functions(see [10), which is a generalization of nearly subconvexlike functions introduced in [34]. We present alternative theorem and derived scalarization theorems for approximate solutions with generalized subconvexlike set-valued maps. And then, Lagrange multiplier theorems under generalized Slater constraint qualification are established.