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

Jayswal Anurag, Baranwal Ayushi, Arana-Jiménez Manuel

Archives of Control Sciences

2024

Vol. 34, No. 2

349--377

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.