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

作　　者：曾静[1] 丁若文 ZENG Jing;DING Ruowen(Schoolof Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《运筹学学报》2023年第3期121-128,共8页Operations Research Transactions

基　　金：国家自然科学基金青年基金(No.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(No.cstc2019jcyj-msxmX0605);重庆市教委科学技术研究项目(No.KJQN201800837);重庆市研究生导师团队建设项目(No.yds223010);重庆工商大学创新团队项目(No.ZDPTTD201908);重庆工商大学研究生创新型科研项目(No.yjscxx2022-112-74)。

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。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.

关 键 词：非凸优化 Painlevé-Kuratowski收敛 稳定性 真拟C-凹 C-凸 

分 类 号：O221.2[理学—运筹学与控制论]