数学季刊 ›› 2010, Vol. 25 ›› Issue (1): 104-109.

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集值映射向量优化的ε-强有效解

  

  1. College of Sciences, Chongqing Jiaotong Unversity ; College of Mathematics and Science, Chongqing University

  • 收稿日期:2007-03-29 出版日期:2010-03-30 发布日期:2023-06-12
  • 作者简介:WANG Qi-lin(1971- ), male, native of Chongqing, a lecturer of Chongqing Jiaotong University, M.S.D., engages in vector optimization.
  • 基金资助:
     Supported by the Natural Science Foundation of China(10871216); Supported by the Natural Science Foundation Project of CQ CSTC(2008BB0346,2007BB0441); Supported by the Excellent Young Teachers Program of Chongqing Jiaotong University(EYT08-016);

ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps

  1. College of Sciences, Chongqing Jiaotong Unversity ; College of Mathematics and Science, Chongqing University

  • Received:2007-03-29 Online:2010-03-30 Published:2023-06-12
  • About author:WANG Qi-lin(1971- ), male, native of Chongqing, a lecturer of Chongqing Jiaotong University, M.S.D., engages in vector optimization.
  • Supported by:
     Supported by the Natural Science Foundation of China(10871216); Supported by the Natural Science Foundation Project of CQ CSTC(2008BB0346,2007BB0441); Supported by the Excellent Young Teachers Program of Chongqing Jiaotong University(EYT08-016);

摘要: In locally convex Hausdorff topological vector spaces, ε-strongly efficient solutions for vector optimization with set-valued maps are discussed. Firstly, ε-strongly efficient point of set is introduced. Secondly, under the nearly cone-subconvex like set-valued maps, the theorem of scalarization for vector optimization is obtained. Finally, optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

关键词: vector optimization, ε-strongly efficient point, nearly cone-subconvex like set-valued maps, ε-strongly efficient solutions, the theorem of scalarization, optimality conditions

Abstract: In locally convex Hausdorff topological vector spaces, ε-strongly efficient solutions for vector optimization with set-valued maps are discussed. Firstly, ε-strongly efficient point of set is introduced. Secondly, under the nearly cone-subconvex like set-valued maps, the theorem of scalarization for vector optimization is obtained. Finally, optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

Key words: vector optimization, ε-strongly efficient point, nearly cone-subconvex like set-valued maps, ε-strongly efficient solutions, the theorem of scalarization, optimality conditions

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