Robust controlled vector variational inequalities for multi-dimensional fractional control optimization problems

Abstract

This paper is devoted to study robust efficiency in terms of variational inequality for a class of multi-dimensional multi-objective first-order PDE-constrained fractional control optimization problems with data uncertainty (MMFP). We derive a robust controlled vector variational inequality (VI) together with its weak form and discuss equivalence between the solutions of (VI) and (MMFP) via imposing the suitable assumptions. Later on, we study a sufficient condition for the robust weak efficient solution of (MMFP) to be its robust efficient solution under the strict convexity assumption and give some applications to illustrate the established results.

Keywords

• fractional control optimization problem
• convexity
• robust efficient solution
• uncertainty
• variational inequality