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Wen, Zhang; Xianjun, Long; Yingquan, Huang; Li, Genghua

Duality and saddle point theorems of approximate solutions for nonsmooth semi-infinite multiobjective optimization problems. (Chinese. English summary) Zbl 07801751

Acta Math. Appl. Sin. 46, No. 4, 532-548 (2023).
Summary: In this paper, a class of nonsmooth semi-infinite multiobjective programming problems is considered by using tangential subdifferentials, and its dual and saddle theorems are discussed. Firstly, Mond-Weir type dual of semi-infinite multiobjective programming problems is established, under the assumptions of the generalized convexity, the weak duality, strong duality and inverse duality theorems of approximate solutions for semi-infinite multiobjective optimization problems are given. Secondly, the \(\varepsilon\)-quasi-saddle of vector Langrange function is defined, then some necessary and sufficient conditions of the \(\varepsilon\)-quasi-saddle point are derived. Our results extend and improve some known results, some examples are given to illustrate the main results of this paper.

MSC:

90C29 Multi-objective and goal programming
90C34 Semi-infinite programming
90C46 Optimality conditions and duality in mathematical programming
49N15 Duality theory (optimization)

Keywords:

semi-infinite multi-objective optimization; tangential subdifferentials; approximate solution; duality; \(\varepsilon\)-quasi-saddle point
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