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向量优化问题的一类非线性标量化定理

唐莉萍1  杨新民2,*   

  1. 1. 重庆工商大学数学与统计学院, 重庆 400067； 2. 重庆师范大学数学科学学院, 重庆 400047
  • 收稿日期:2015-01-14 出版日期:2016-09-15 发布日期:2016-09-15
  • 通讯作者: 杨新民 xmyang@cqnu.edu.cn
  • 基金资助:

    国家自然科学基金(Nos. 11431004, 11271391), 重庆市科委项目(Nos. cstc2016jcyjA0178, cstc2015jcyjB00001, cstc2014pt-sy00001), 重庆市教委项目(No. KJ1600613), 重庆工商大学校级项目(No. 670101574)

A class of nonlinear scalarization theorem of vector optimization problems

TANG Liping1  YANG Xinmin2,*   

  1. 1. College of Mathematics and Statistics, Chongqing Technology and Business University,  Chongqing 400067, China; 2. College of Mathematics Sciences, Chongqing Normal University, Chongqing 400047, China
  • Received:2015-01-14 Online:2016-09-15 Published:2016-09-15

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摘要：

利用Gertewitz泛函研究向量优化问题的一类非线性标量化问题. 证明了向量优化问题的(C, \varepsilon)-弱有效解或(C, \varepsilon)-有效解与标量化问题的近似解或严格近似解间的等价关系, 并估计了标量化问题的近似解．

关键词: 向量优化, 非线性标量化, Gertewitz泛函, (C, \varepsilon)-有效解, (C, \varepsilon)-弱有效解

Abstract:

In this paper, a class of nonlinear scalarization for vector optimization problem is investigated via Gertewitz functional. We mainly prove the fact that (C, \varepsilon)-weakly efficient solutions or (C, \varepsilon)-efficient solutions of vector optimization problem are equivalent to approximate solutions or strictly approximate solutions of scalar problem, and also  estimate the approximate solutions of this scalar problem.

Key words: vector optimization, nonlinear scalarization, Gertewitz functional, (C, \varepsilon)-efficient solution, (C, \varepsilon)-weakly efficient solution