非光滑半无限多目标优化问题的对偶性

doi:10.12341/jssms13215

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (7): 1633-1645.DOI: 10.12341/jssms13215

非光滑半无限多目标优化问题的对偶性

杨玉红^1,2，唐莉萍³

1.内蒙古大学数学科学学院, 呼和浩特 010021; 2. 长江师范学院数学与统计学院, 重庆 408100;3. 重庆工商大学数学与统计学院,重庆 400067

出版日期:2017-07-25 发布日期:2017-09-30

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杨玉红，唐莉萍. 非光滑半无限多目标优化问题的对偶性[J]. 系统科学与数学, 2017, 37(7): 1633-1645.

YANG Yuhong, TANG Liping. Duality for Nonsmooth Semi-Infinite Multiobjective Optimization Problems[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(7): 1633-1645.

Duality for Nonsmooth Semi-Infinite Multiobjective Optimization Problems

YANG Yuhong ^1,2 ,TANG Liping³

1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021; 2. School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100; 3. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Online:2017-07-25 Published:2017-09-30

研究了一个非光滑半无限多目标优化问题(简记为SIMOP)并讨论它的对偶性. 本文重点考虑此SIMOP的Mond-Weir型半无限多目标对偶问题, 通过对目标函数和约束函数的某种组合赋予Clarke $F$-凸性假设, 获得了弱/强/逆对偶结论. 文章的一些结论是比较新的, 并推广了已有文献的一些结果.

关键词： 半无限多目标优化, 对偶性, (弱)有效解, Clarke $F$-凸性.

This paper deals with a nonsmooth semi-infinite multiobjective optimization problem (SIMOP, in brief) and discusses its duality. We focus on Mond-Weir type semi-infinite multiobjective dual problem of the SIMOP, and weak/strong/ converse duality results are obtained by imposing Clarke $F$-convexity hypotheses on some combinations of objective functions and constraint functions. Some of our results are new and generalize the conclusions in some former literatures.

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