Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems

In this paper, for a robust nonsmooth semi-infinite objective optimization problem associated with data uncertainty, some constraint qualifications (CQs): Abadie CQ, Mangasarian-Fromovitz CQ, and Pshenichnyi-Levin-Valadire CQ are proposed. Sufficient conditions for them are also derived. Under these CQs, we establish both necessary and sufficient conditions for robust weak Pareto, Pareto, and Benson proper solutions. These conditions are the forms of Karush-Kuhn-Tucker rule. Moreover, the Wolfe and Mond-Weir duality schemes are also addressed. Finally, we employ the obtained results to present some conditions for linear programming. Examples are provided for analyzing and illustrating our results.

Automated summary

This paper investigates a robust nonsmooth semi-infinite objective optimization problem associated with data uncertainty. It proposes some constraint qualifications and derives sufficient conditions for them. Necessary and sufficient conditions for robust weak Pareto, Pareto, and Benson proper solutions are established under these conditions. The paper also addresses the Wolfe and Mond-Weir duality schemes and presents conditions for linear programming using the obtained results.