On the Existence of Super Efficient Solutions and Optimality Conditions for Set-Valued Vector Optimization Problems

Abstract

In this paper, by using the normal subdifferential and equilibrium-like function we first obtain some properties for K-preinvex set-valued maps. Secondly, in terms of this equilibrium-like function, we establish some sufficient conditions for the existence of super minimal points of a K-preinvex set-valued map, that is, super efficient solutions of a set-valued vector optimization problem, and also attain necessity optimality terms for a general type of super efficiency.

Keywords

• <i>K</i>-preinvex multi-valued map
• normal subdifferential
• equilibrium-like function
• set-valued vector optimization problem
• super efficient solutions