WEAK E-OPTIMAL SOLUTION IN VECTOR OPTIMIZATION

Abstract

In a real locally convex Hausdorff topological vector space, we first introduce the concept of nearly $E$-subconvexlikeness of set-valued maps via improvement set and obtain an alternative theorem. Furthermore, under the assumption of nearly subconvexlikeness, we establish scalarization theorem, Lagrange multiplier theorem, weak $E$-saddle point criteria and weak $E$-duality for weak $E$-optimal solution in vector optimization with set-valued maps. We also propose some examples to illustrate the main results.