On vector variational E-inequalities and differentiable vector optimization problem

Abstract

Abstract In this paper, in order to characterize optimality of a class of nonconvex differentiable multiobjective programming problems, we introduce two new types of vector variational-like inequalities, namely, a weak variational E -inequality and a vector variational E -inequality. Namely, under (strictly) E -convexity, we prove relationships between the aforesaid vector variational-like inequalities and differentiable vector optimization problems. Further, under (strictly) pseudo- E -convexity, we are in position to identify vector critical E -points, weak E -Pareto ( E -Pareto) solutions of differentiable vector optimization problems and solutions of these introduced vector variational-like inequalities.