| 引用本文: | 张雯, 龙宪军, 黄应全.非凸半无限多目标规划近似解的最优性条件(J/M/D/N,J:杂志，M：书，D：论文，N：报纸).期刊名称,2022，39（3）：41-46 |
| CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435 |
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| 摘要: |
| 针对一类非凸半无限多目标规划问题,建立了其近似解的最优性条件。 借助切向次微分定义了 新的正则条件以及广义不变凸函数,值得注意的是,涉及的函数并不需要满足局部 Lipschitz 条件。 首先,给 出半无限多目标规划问题的(η,ε)-拟弱有效解和(η,ε)-拟有效解的定义,在正则条件的假设下,获得(η, ε)-拟弱有效解的必要最优性条件;然后,在广义不变凸性假设下,获得(η,ε)-拟(弱)有效解的充分最优性 条件;所得结果推广和改进了相关文献的主要结论。 |
| 关键词: 半无限多目标规划 (η,ε)-拟弱有效解 切向次微分 广义不变凸函数 |
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| Optimality Conditions for Approximate Solutions of Nonconvex Semi-infinite Multiobjective Programming |
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ZHANG Wen, LONG Xian-jun, HUANG Ying-quan
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School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
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| Abstract: |
| Optimality conditions of approximate solutions for nonconvex semi-infinite multiobjective programming problem are established. By means of tangential subdifferential, some new regular conditions and generalized invex functions are defined. It’ s worth noting that the functions involved are not necessarily local Lipschitz. The definitions of (η,ε)-quasi weakly efficient solutions and (η,ε)-quasi efficient solutions for semi- infinite multiobjective programming problems are introduced. By the regular conditions, the necessary optimality condition of (η,ε)-quasi weakly efficient solutions is obtained. Moreover, the sufficient optimality condition of (η,ε)-quasi (weakly) efficient solutions is proposed by the generalized invex convexity. The results obtained in this paper improve and generalize the corresponding results in the literature. |
| Key words: semi-infinite multi-objective programming ( η, ε)-quasi weakly effective solution tangential subdifferential generalized invex functions |
