华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (3): 59-67.

• 应用数学与基础数学 • 上一篇    下一篇

非凸集值优化问题弱Benson真有效解的高阶最优性条件

王开荣;王义利;曹 伟   

  1. 重庆大学 数学与统计学院, 重庆 401331
  • 收稿日期:2010-05-01 修回日期:2010-08-01 出版日期:2011-05-25 发布日期:2011-05-25
  • 通讯作者: 王开荣

Higher order optimality conditions for weakly Benson proper efficient solutions of nonconvex set-valued optimization problems

WANG Kai-rong;WANG Yi-li;CAO Wei   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2010-05-01 Revised:2010-08-01 Online:2011-05-25 Published:2011-05-25
  • Contact: WANG Kai-rong

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摘要： 首先, 给出了一些必要的基 本概念和重要引理. 其次, 讨论了高阶广义切集的一些重要性质. 最后, 利用这些性质和Gerstewitz 非凸分离泛函, 在目标映射以及约束映射没有任何凸性假设的条件下, 获得了带广义不等式约束的 集值优化问题弱Benson真有效解的高阶必要和充分最优性条件. 同时, 给出例子说明了所获得的结果推广了文献中的相应结果.

关键词: 集值优化, 广义高阶相依集, 非凸分离泛函, Benson真有效解, 高阶最优性条件, 集值优化, 广义高阶相依集, 非凸分离泛函, Benson真有效解, 高阶最优性条件

Abstract: Firstly, some necessarily basic concepts and an important lemma were given. Secondly, some important properties of generalized higher-order tangent sets were discussed. Finally, by virtue of those properties and the Gerstewitz's nonconvex separation functional, necessary and sufficient optimality conditions were obtained for weakly Benson proper efficient solutions of set-valued optimization problems without any convexity assumption on objective
and constraint mappings. Moreover, two examples were given to show that the result obtained is a generalization to the corresponding results in literatures.

Key words: generalized higher order contingent sets, nonconvex separation functional, Benson proper efficient solutions, higher-order optimality conditions, set-valued optimization, generalized higher order contingent sets, nonconvex separation functional, Benson proper efficient solutions, higher-order optimality conditions

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