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运筹学学报 ›› 2018, Vol. 22 ›› Issue (3): 79-88.doi: 10.15960/j.cnki.issn.1007-6093.2018.03.008

• 运筹学 • 上一篇    下一篇

含参广义集值向量均衡问题有效解映射下半连续的最优条件

孟旭东1,* 王三华2  龚循华2   

  1. 1. 南昌航空大学科技学院, 南昌 330034; 2. 南昌大学数学系, 南昌 330031
  • 收稿日期:2016-05-31 出版日期:2018-09-15 发布日期:2018-09-15
  • 通讯作者: 孟旭东 E-mail: xudong88m@163.com
  • 基金资助:

    国家自然科学基金(Nos. 11061023, 11201216), 中国博士后科学基金(No. 2015M582047), 江西省青年基金(No. GJJ161597)

Optimal conditions for the lower semicontionuity of efficient solution mapping to parametric generalized set-vector equilibrium problems

MENG Xudong1,*  WANG Sanhua2  GONG Xunhua2   

  1. 1. Science and Technology College of Nanchang Hangkong University, Nanchang 330034, China 2. School of Sciences, Nanchang University, Nanchang 330031, China
  • Received:2016-05-31 Online:2018-09-15 Published:2018-09-15

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摘要：

在实Hausdorff拓扑向量空间中研究一类含参广义集值向量均衡问题弱有效解与有效解映射的下半连续性. 在近似锥-次类凸的条件下, 运用标量化的方法得到弱有效解的标量化结果. 在适当条件下, 得到含参广义集值向量均衡问题弱有效解与有效解映射下半连续性定理.

关键词: 弱有效解, 有效解, 解映射, 下半连续性, 含参广义集值向量均衡问题

Abstract:

The lower semicontionuity of weak efficient solution and efficient solution mappings to a class of parametric generalized set-vector equilibrium problems in real Hausdorff topological vector spaces are studied. Under the condition of nearly cone-subconvexlike, scalar characterization of weak efficient solution is given by using the scalar method. Under some suitable assumptions, the lower semicontionuity theorem of weak efficient solution and efficient solution mappings to the parametric generalized set-vector equilibrium problems are gained.

Key words: weak efficient solution, efficient solution, solution mapping, lower semicontionuity, parametric generalized set-vector equilibrium problems