向量优化问题Benson真有效解的稳定性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 35-44.

向量优化问题Benson真有效解的稳定性

曾静(),胡瑞婷*()

重庆工商大学数学与统计学院重庆 400067

收稿日期:2021-01-27 出版日期:2022-02-01 发布日期:2022-02-23
通讯作者: 胡瑞婷 E-mail:zengjing1983@ctbu.edu.cn;zengjing1983@ctbu.edu.cn; 943389111@qq.com
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项目(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)

Stability of Benson Proper Efficient Solutions for Vector Optimization Problems

Jing Zeng(),Ruiting Hu*()

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received:2021-01-27 Online:2022-02-01 Published:2022-02-23
Contact: Ruiting Hu E-mail:zengjing1983@ctbu.edu.cn;zengjing1983@ctbu.edu.cn; 943389111@qq.com
Supported by:
the NSFC(12001445);the General Project of Chongqing NSF(Special Project of Basic Research and Frontier Exploration)(cstc2019jcyj-msxmX0605);the Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJQN201800837)

摘要/Abstract

摘要：

首先利用非线性标量化技术，建立了向量优化问题Benson真有效解与一类标量优化问题解之间的等价关系.然后借助建立的等价性结果，在向量优化问题目标映射和约束条件均扰动的情况下，得到了向量优化问题Benson真有效点集和解集的抗干扰稳定性结果.该结果首次借助标量化技术，在扰动问题序列Painlevé-Kuratowski收敛于目标优化问题的情况下，研究了向量优化问题Benson真有效解的抗干扰性，该结果对数值计算分析有重要的理论价值.

关键词: Benson真有效解, Painlevé-Kuratowski收敛, 标量化, 稳定性

Abstract:

In this paper, at the beginning, we established the equivalent relationship between Benson proper efficient solutions of vector optimization problems and the solution of a class of scalar optimization problems by using nonlinear scaling technique. Besides, with the means of the equivalence result, we obtained the anti-interference stability results of Benson proper efficient point sets and the solution sets in the vector optimization problem when the objective function and the constraint conditions were perturbed. For the first time, by the means of the scalarization technique, we study the anti-interference of Benson proper efficient solutions of vector optimization problems under the condition that the disturbance problem sequence Painlevé-Kuratowski converges to the object optimization problem. And the results have important theoretical value for numerical calculation and analysis.

Key words: Benson proper efficient solution, Painlevé-Kuratowski convergence, Scalarization, Stability

中图分类号:

O224

曾静,胡瑞婷. 向量优化问题Benson真有效解的稳定性[J]. 数学物理学报, 2022, 42(1): 35-44.

Jing Zeng,Ruiting Hu. Stability of Benson Proper Efficient Solutions for Vector Optimization Problems[J]. Acta mathematica scientia,Series A, 2022, 42(1): 35-44.

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