Second-order optimality conditions with the envelope-like effect for nonsmooth vector optimization in infinite dimensions |
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| Affiliation: | 1. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Viet Nam;2. Department of Mathematics and Statistics, University of Economics of Hochiminh City, 59C Nguyen Dinh Chieu, D.3, Hochiminh City, Viet Nam;1. Department of Optimization and Control Theory, Institutes of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet road, Hanoi, Vietnam;2. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam;3. Department of Mathematics, Hangzhou Normal University, Hangzhou, China;4. Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan;5. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan;6. Center for General Education, China Medical University, Taichung 40402, Taiwan;1. IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil;2. Dipartimento di Matematica, Università di Padova, Via Trieste 63, Padova 35121, Italy;1. School of Mathematics, Dongbei University of Finance and Economics, Dalian 116025, China;2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;1. D.I.I.E.S., Mediterranean University of Reggio Calabria, Loc. Feo di Vito, 89122 Reggio Calabria, Italy;2. Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 6, Catania, 95125, Italy;1. Department of Mathematics and Applications, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal;2. Centre of Mathematics, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal |
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| Abstract: | Second-order necessary conditions and sufficient conditions with the envelope-like effect for optimality in nonsmooth vector optimization are established. We use approximations as generalized derivatives, imposing strict differentiability for necessary conditions and differentiability for sufficient conditions and avoiding continuous differentiability. Convexity conditions are not imposed explicitly. The results make it clear when the envelope-like effect occurs and improve or include several recent existing ones. Examples are provided to show advantages of our theorems over some known ones in the literature. |
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