向量优化问题Benson真有效解的稳定性  

Stability of Benson Proper Efficient Solutions for Vector Optimization Problems

作　　者：曾静[1] 胡瑞婷 Jing Zeng;Ruiting Hu(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《数学物理学报（A辑）》2022年第1期35-44,共10页Acta Mathematica Scientia

基　　金：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)。

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Painleve-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.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 Painleve-Kuratowski converges to the object optimization problem.And the results have important theoretical value for numerical calculation and analysis.

关 键 词：BENSON真有效解 Painlevé-Kuratowski收敛 标量化 稳定性 

分 类 号：O224[理学—运筹学与控制论]