On some vector variational inequalities and optimization problems

Abstract

This paper establishes connections between the solutions of some new vector controlled variational inequalities and (proper) efficient solutions of the corresponding multiobjective controlled variational problem. More precisely, under the assumptions of invexity and Fréchet differentiability of the involved curvilinear integral functionals, and by using the notion of invex set with respect to some given functions, we derive the characterization results.

Keywords

• (proper) efficient solution
• invex set
• fréchet differentiability
• curvilinear integral