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

Abstract

Thispaperisdevotedtostudyrobustefficiencyintermsofvariationalinequalityforaclassof 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.