Generalized convex functions and vector variational inequalities

Abstract

In this paper, (α, φ,Q)-invexity is introduced, where α:X ×X → intRm+, φ:X ×X →X,X is a Banach space,Q is a convex cone ofRm. This unifies the properties of many classes of functions, such asQ-convexity, pseudo-linearity, representation condition, null space condition, andV-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (α, φ,Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (α, φ,Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.