Berge-type theorems for vector optimization problems

Abstract

In the present paper we investigate continuity properties of the minimal point multivalued mapping associated with parametric vector optimization problems in topological vector spaces. This mapping can be viewed as a counterpart of the optimal value function in scalar optimization. We prove sufficient conditions for several types of continuities of minimal points and discuss their relationship to the existing results as well to the classical Berge Maximum Theorems in the case of scalar optimization problems

Keywords:

• Vector Optimization
• Parametric Vector Optimization
• Continuity of Minimal Points