Necessary conditions for extremality and separation theorems with applications to multiobjective optimization

Abstract

The aim of this paper is to give necessary conditions for extremality in terms of an abstract subdifferential and to obtain general separation theorems including both finite and infinite classical separation theorems. This approach, which is mainly based on Ekeland's variational principle and the concept of locally weak-star compact cones, can be considered as a generalization f the notions of optima in problems of scalar or vector optimization with and without constraints. The results obtained are applied to derive new necessary optimality conditions for Pareto local minimum and weak Pareto minimum of nonsmooth multlobjectivep rogramming problems.

Keywords:

• Efficiency
• Extremality: Ekeland's Variational Principle
• Separation Theorems
• Local Compactness
• Subdlfferentials
• Multiobjective Programming