数学季刊 ›› 2010, Vol. 25 ›› Issue (1): 132-139.

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Hausdorff拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性

  

  1. School of Mathematics and Information Science, Wenzhou University
  • 收稿日期:2006-03-30 出版日期:2010-03-30 发布日期:2023-06-13
  • 作者简介:ZHOU Xuan-wei(1963- ), male, native of Wenzhou, Zhejiang, a professor of Wenzhou University, Ph.D., engages in multiobjective optimization.
  • 基金资助:
     Supported by the National Natural Science Foundation of China(70071026);

Connectedness of Cone-efficient Solution Set for Cone-quasiconvex Multiobjective Programming in Hausdorff Topological Vector Spaces 

  1. School of Mathematics and Information Science, Wenzhou University

  • Received:2006-03-30 Online:2010-03-30 Published:2023-06-13
  • About author:ZHOU Xuan-wei(1963- ), male, native of Wenzhou, Zhejiang, a professor of Wenzhou University, Ph.D., engages in multiobjective optimization.
  • Supported by:
     Supported by the National Natural Science Foundation of China(70071026);

摘要: This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.

关键词: multiobjective programming, cone-efficient solution, cone-quasiconvex map

Abstract: This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.

Key words: multiobjective programming, cone-efficient solution, cone-quasiconvex map

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