On approximate starshapedness in multiobjective optimization

Abstract

In this paper, we give the vector versions of the concepts of approximate starshapedness, equisubdifferentiability and pseudo-equi-subdifferentiability and establish relationships among approximate vector starshapedness, vector-equi-subdifferentiability and vector-pseudo-equi-subdifferentiability. We extend the concept of -quasi-efficient solutions in the context of multiobjective optimization problems involving approximately starshaped functions and use approximate vector variational inequalities of Stampacchia and Minty type in terms of Fréchet subdifferentials to characterize approximate efficient solutions.

Optimality and Duality of Approximate Quasi Weakly Efficient Solution for Nonsmooth Vector Optimization Problems

“…Until now, the concepts of invexity (see [9]), pseudo-convexity, and quasi-convexity (see [10]) had been introduced, and the optimality conditions for di erent e cient solutions to vector optimization problems had been discussed. For more references dealing with approximate solutions and approximate convexity, please refer to [11][12][13][14]. In this paper, we will propose a kind of generalized convexity, termed as the approximate pseudo quasi type-I functions, and use it to explore optimality to the problem (VOP) with respect to the approximate quasi weakly e ciency.…”