Journal of Convex Analysis 31 (2024), No. 3, 999--1020
Copyright Heldermann Verlag 2024
Second-Order Optimality Conditions for Efficiency in C1-Smooth Robustly Quasiconvex Multiobjective Programming Problems
Tran Van Su
Faculty of Mathematics, The University of Danang, University of Science and Education, Da Nang, Vietnam
tvsu@ued.udn.vn
Dinh Dieu Hang
Faculty of Natural Sciences, Electric Power University, Hoang Quoc Viet, Hanoi, Vietnam
hangdd@epu.edu.vn
We study some second-order optimality conditions in terms of second-order Mordukhovich's subdifferentials for the weak efficiency of C1-smooth robustly quasiconvex multiobjective programming problem with set, inequality and equality constraints. We provide some second-order generalized constraint qualifications and two necessary conditions for the robust quasiconvexity of C1-smooth / C1,1-smooth mappings. Using this result, weak and strong second-order Karush-Kuhn-Tucker-type necessary optimality conditions in terms of Mordukhovich's subdifferentials / Fréchet's subdifferentials are provided. Under some suitable assumptions, some second-order Karush-Kuhn-Tucker type sufficient optimality conditions are presented too. Examples demonstrate the applicability of the obtained results.
Keywords: C1-smooth robustly quasiconvex multiobjective programming, constraints, weak efficiency, KKT-type second-order optimality conditions, second-order constraint qualifications, second-order Mordukhovich's subdifferential.
MSC: 90C46, 90C29, 49K27, 49J52.
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