ZHANG Wen, LONG Xian-jun, HUANG Ying-quan.Optimality Conditions for Approximate Solutions of Nonconvex Semi-infinite Multiobjective Programming[J].Journal of Chongqing Technology and Business University(Natural Science Edition）,2022,39(3):41-46

Optimality Conditions for Approximate Solutions of Nonconvex Semi-infinite Multiobjective Programming

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 作者 单位 张雯, 龙宪军, 黄应全 重庆工商大学数学与统计学院, 重庆 400067

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。

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.