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

Nguyen Minh Tung () and Mai Duy ()
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Nguyen Minh Tung: Banking University of Ho Chi Minh City
Mai Duy: FPT University

4OR, 2023, vol. 21, issue 1, No 6, 176 pages

Abstract: Abstract 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.

Keywords: Robust multiobjective optimization; Semi-infinite optimization; Optimality condition; Duality; Constraint qualification; 90C29; 90C34; 90C46 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10288-022-00506-4

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