On V-r-invexity and vector variational-like inequalities

Abstract

In this paper, we consider the multiobjective optimization problems involving the differentiable V-r-invex vector valued functions. Under the assumption of V-r-invexity, we use the Stampacchia type vector variational-like inequalities as tool to solve the vector optimization problems. We establish equivalence among the vector critical points, the weak efficient solutions and the solutions of the Stampacchia type weak vector variational-like inequality problems using Gordan's separation theorem under the V-r-invexity assumptions. These conditions are more general than those appearing in the literature.