Robust Efficiency Conditions in Multiple-Objective Fractional Variational Control Problems

Abstract

The aim of this study is to investigate multi-dimensional vector variational problems considering data uncertainty in each of the objective functional and constraints. We establish the robust necessary and sufficient efficiency conditions such that any robust feasible solution could be the robust weakly efficient solution for the problems under consideration. Emphatically, we present robust efficiency conditions for multi-dimensional scalar, vector, and vector fractional variational problems by using the notion of a convex functional.

Characterization Results of Solution Sets Associated with Multiple-Objective Fractional Optimal Control Problems

“…In this section, by using the robust necessary efficiency conditions established in Ritu et al [25], we investigate robust weak, robust strong, and robust strict converse-type duality results. More precisely, by considering the Wolfe-and Mond-Weir-type dualities, we formulate a robust mixed-type dual problem, and, under suitable convexity assumptions of the involved functionals, we establish some equivalence results between the solution sets of the considered models.…”

“…More specifically, this paper is essentially a natural continuation of the studies stated in Mititelu and Treanţȃ [20] and Ritu et al [25]. In this regard, by using the robust necessary efficiency conditions established in Ritu et al [25], we investigate robust weak, robust strong, and robust strict converse-type duality results. The limitations of the existing works and the main credits of this paper are the following: (i) the presence of mixed constraints involving partial derivatives, (ii) the presence of the uncertainty data both in the cost functionals but also in the constraint functionals, and (iii) the combination of parametric and robust approaches to study the considered class of problems.…”

“…The robust multiple objective fractional optimal control problem is formulated (see, also, Mititelu and Treanţȃ [20], Treanţȃ and Mititelu [24], and Ritu et al [25]) as:…”

“…On adding the inequalities ( 23), (25), and (26), we obtain the following inequality: S ( λ − ῑ){ ηT ∂h ∂λ ( Π, ς) − Q 0 ∂z ∂λ ( Π, γ) + ρT f λ ( Π, ῑα (t), σ)…”

“…In this paper, under the motivation of the above-mentioned research papers and by considering suitable convexity hypotheses for the involved integral-like functionals, a mixed-type dual model is developed for the multiple objective fractional optimal control problem determined by multiple integral functionals defined in Ritu et al [25]. More specifically, this paper is essentially a natural continuation of the studies stated in Mititelu and Treanţȃ [20] and Ritu et al [25]. In this regard, by using the robust necessary efficiency conditions established in Ritu et al [25], we investigate robust weak, robust strong, and robust strict converse-type duality results.…”