一类带映射差的非凸向量优化问题解的稳定性

doi:10.15960/j.cnki.issn.1007-6093.2023.03.009

运筹学学报 ›› 2023, Vol. 27 ›› Issue (3): 121-128.doi: 10.15960/j.cnki.issn.1007-6093.2023.03.009

一类带映射差的非凸向量优化问题解的稳定性

曾静¹^,*(), 丁若文¹

1. 重庆工商大学数学与统计学院, 重庆 400067

收稿日期:2022-01-28 出版日期:2023-09-15 发布日期:2023-09-14
通讯作者: 曾静 E-mail:zengjing1983@ctbu.edu.cn
作者简介:曾静, E-mail: zengjing1983@ctbu.edu.cn
基金资助:
国家自然科学基金青年基金(12001445);重庆市自然科学基金(基础研究与前沿探索专项)面上项目(cstc2019jcyj-msxmX0605);重庆市教委科学技术研究项目(KJQN201800837);重庆市研究生导师团队建设项目(yds223010);重庆工商大学创新团队项目(ZDPTTD201908);重庆工商大学研究生创新型科研项目(yjscxx2022-112-74)

Stability of solutions for a class of non-convex vector optimization problems with mapping differences

Jing ZENG¹^,*(), Ruowen DING¹

1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received:2022-01-28 Online:2023-09-15 Published:2023-09-14
Contact: Jing ZENG E-mail:zengjing1983@ctbu.edu.cn

摘要/Abstract

摘要：

在实际生活中，问题数据常常受到干扰，求原问题解时，常常利用近似问题解去逼近原问题解。使用这种方法进行求解时，原问题解集的稳定性是一个重要的前提条件。本文考虑一类带映射差的非凸向量优化问题，研究了近似问题数据收敛于原问题数据时，通过对映射差的两个映射凸性和收敛性的限制，获得了带映射差的非凸向量优化问题在Painlevé-Kuratowski收敛性意义下有效解的稳定性结果。

关键词: 非凸优化, Painlevé-Kuratowski收敛, 稳定性, 真拟$C$-凹, $C$-凸

Abstract:

The data of problem are often perturbed in real life. We often calculate the solution of a perturbed problem to approximate the original problem solution. Therefore, the stability of the solution set of the original problem is an important issue. In this paper, we consider a class of non-convex vector optimization problems with two mapping differences. By taking advantage of appropriate convergence and convexity of the two mappings, the stability results of the nonconvex vector optimization problem is obtained, when the approximate problem data converge to the original problem data in the sense of Painlevé-Kuratowski's convergence.

Key words: non-convex optimization, Painlevé-Kuratowski convergence, stability, properly quasi $C$-concave, $C$-convex

中图分类号:

O221.2

曾静, 丁若文. 一类带映射差的非凸向量优化问题解的稳定性[J]. 运筹学学报, 2023, 27(3): 121-128.

Jing ZENG, Ruowen DING. Stability of solutions for a class of non-convex vector optimization problems with mapping differences[J]. Operations Research Transactions, 2023, 27(3): 121-128.

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一类带映射差的非凸向量优化问题解的稳定性

Stability of solutions for a class of non-convex vector optimization problems with mapping differences

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