Geodesic
Second-Order Optimality Conditions for Efficiency in C1-Smooth Robustly Quasiconvex Multiobjective Programming Problems
Journal of convex analysis, Tome 31 (2024) no. 3, pp. 999-102
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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.
Classification : 90C46, 90C29, 49K27, 49J52
Mots-clés : C1-smooth robustly quasiconvex multiobjective programming, constraints, weak efficiency, KKT-type second-order optimality conditions, second-order constraint qualifications, second-order Mordukhovich's subdifferential 
@article{JCA_2024_31_3_JCA_2024_31_3_a13,
     author = {T. V. Su and D. D. Hang},
     title = {Second-Order {Optimality} {Conditions} for {Efficiency} in {C\protect\textsuperscript{1}-Smooth} {Robustly} {Quasiconvex} {Multiobjective} {Programming} {Problems}},
     journal = {Journal of convex analysis},
     pages = {999--102},
     year = {2024},
     volume = {31},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2024_31_3_JCA_2024_31_3_a13/}
}
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T. V. Su; D. D. Hang. Second-Order Optimality Conditions for Efficiency in C1-Smooth Robustly Quasiconvex Multiobjective Programming Problems. Journal of convex analysis, Tome 31 (2024) no. 3, pp. 999-102. http://geodesic.mathdoc.fr/item/JCA_2024_31_3_JCA_2024_31_3_a13/