Abstract

We study some second-order optimality conditions in terms of second-order Mordukhovich's subdifferentials for the weak efficiency of C1C^1-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 C1C^1-smooth / C1,1C^{1,1}-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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

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

Mathematics Subject Classification

90C46, 90C29, 49K27, 49J52

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Suggested citation

T. V. Su, D. D. Hang. “Second-Order Optimality Conditions for Efficiency in C^1-Smooth Robustly Quasiconvex Multiobjective Programming Problems.” Journal of Convex Analysis 31 (2024), No. 3, 999–1020. https://doi.org/10.68381/jca31048

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