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向量优化问题的近似解研究

杨新民1,*   赵克全1   

  1. 1. 重庆师范大学数学科学学院, 重庆 401331
  • 收稿日期:2017-09-14 出版日期:2017-12-15 发布日期:2017-12-15
  • 通讯作者: 杨新民 xmyang@cqnu.edu.cn
  • 基金资助:

    国家自然科学基金重点项目(No. 11431004), 国家自然科学基金面上项目(Nos. 11271391, 11671062), 重庆市基础与前沿研究计划项目(No.cstc2015jcyjA00027), 重庆市教委科学技术研究项目(No. KJ1500303)

Study on approximate solutions of vector optimization problems

YANG Xinmin1,*   ZHAO Kequan1   

  1. 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
  • Received:2017-09-14 Online:2017-12-15 Published:2017-12-15

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摘要：

向量优化是数学规划领域中十分重要的研究方向之一, 其相关基础理论与基本方法的研究具有非常重要的理论意义与应用价值. 近年来, 关于近似解的定义及其性质研究已成为向量优化理论与方法研究的热点. 现主要介绍国内学者, 特别是我们团队在向量优化问题的各类近似解和统一解概念及其发展和各类近似解与统一解的性质研究方面取得的一些重要进展. 最后, 提出了与向量优化问题的近似解与统一解相关的一些公开问题.

关键词: 向量优化问题, 近似解, 统一解, Co-radiant 集, 改进集

Abstract:

Vector optimization is one of the important research aspects in the field of mathematical programming and some related fundamental theory and basic methods have great theoretical significance and applicable value. In recent years, study on the definitions and properties of approximate solutions has become one research hotspot in theory and methods of vector optimization. In this paper, we mainly review some important progress about some concepts of approximate solutions and unified solutions, and their development and some properties of various kinds of approximate solutions and unified solutions for a class of vector optimization problems by Chinese researchers and especially for our group. In the end, we also propose some open questions related to approximate solutions and unified solutions in vector optimization problems.

Key words: vector optimization problems, approximate solutions, unified solutions, Co-radiant sets, improvement sets