数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1076-1094.

• 论文 • 上一篇    下一篇

多目标约束向量优化问题的类拉格朗日乘数法

李润鑫1(),黄辉2,尚振宏1,曹宇1,王红斌1,*(),张晶1   

  1. 1 昆明理工大学信息工程与自动化学院 昆明 650500
    2 云南大学数学与统计学院 昆明 650091
  • 收稿日期:2016-12-30 出版日期:2018-12-26 发布日期:2018-12-27
  • 通讯作者: 王红斌 E-mail:rxli@kmust.edu.cn;whbin2007@126.com
  • 作者简介:李润鑫, E-mail:rxli@kmust.edu.cn
  • 基金资助:
    国家自然科学基金(11461080);国家自然科学基金(61562051);国家自然科学基金(61462052);国家自然科学基金(61462054);云南省人才培养基金(KKSY201603016)

Lagrange-Like Multiplier Rules for Weak Approximate Pareto Solutions of Multiobjective Constrained Vector Optimization Problems

Runxin Li1(),Hui Huang2,Zhenhong Shang1,Yu Cao1,Hongbin Wang1,*(),Jing Zhang1   

  1. 1 Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500
    2 Department of Mathematics, Yunnan University, Kunming 650091
  • Received:2016-12-30 Online:2018-12-26 Published:2018-12-27
  • Contact: Hongbin Wang E-mail:rxli@kmust.edu.cn;whbin2007@126.com
  • Supported by:
    Supported by the NSFC(11461080);Supported by the NSFC(61562051);Supported by the NSFC(61462052);Supported by the NSFC(61462054);the Yunnan Provincial Foundation for Personnel Cultivation(KKSY201603016)

摘要:

文献[21]给出了实希尔伯特空间中含有一个约束条件的向量优化问题的有关帕雷托解的拉格朗日乘数法.该文把文献[21]中的主要结果推广到了含有任意m个约束条件的多目标向量优化问题中,给出了实希尔伯特空间中,以proximal法锥和目标函数的coderivative刻画的多目标约束向量优化问题的类拉格朗日乘数法.

关键词: 向量优化, Proximal法锥, Coderivative, ε-帕雷托解, 多目标约束向量优化问题

Abstract:

In real Hilbert space case, Zheng and Li[21] established a Lagrange multiplier rule for weak approximate Pareto solutions of constrained vector optimization problems with only one constrained multifunction. In this paper, we improve and extend their main results to multiobjective constrained vector optimization problems' cases.

Key words: Vector optimization, Proximal normal cone, Coderivative, Weak ε-Pareto solution, Multiobjective constrained vector optimization problem

中图分类号: 

  • O29