Duality in Vector Optimization Under Type 1 α-Invexity in Banach Spaces

Abstract

The aim of this paper is to provide global optimality conditions and duality results for a class of nonconvex vector optimization problems posed on Banach spaces. In this paper, we introduce the concept of quasi type I α-invex, pseudo type I α-invex, quasi pseudo type I α-invex, and pseudo quasi type I α-invex functions in the setting of Banach spaces, and we consider a vector optimization problem with functions defined on Banach spaces. A few sufficient optimality conditions are given, and some results on duality are proved.

Keywords:

• Duality
• Nonsmooth programming
• Optimality
• Type I α-invexity
• Vector optimization

AMS Subject Classification:

• 49K27
• 90C46
• 93C25