非凸多目标优化问题有效解集的非空性与有界性的渐近刻画  

Asymptotic Characterization of Non-Emptiness and Boundedness of Efficient Solution Sets for Nonconvex Multi-Objective Optimization Problems

作　　者：刘应 傅小恒 唐莉萍[2] LIU Ying;FU Xiaoheng;TANG Liping(School of Mathematical Sciences,Chongqing Normal University,Chonging 401331,P.R.China;National Center for Applied Mathematics in Chongqing,Chongqing Normal University,Chonging 401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]重庆师范大学重庆国家应用数学中心,重庆401331

出　　处：《应用数学和力学》2025年第4期519-527,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(重大项目)(11991024);国家自然科学基金(面上项目)(12171060);重庆市自然科学基金(ncamc2022-msxm01,CSTB2024NSCQ-LZX0140);重庆市教委重大项目(KJZD-M202300504)。

摘　　要：优化问题解集的非空性和有界性在数值算法研究中发挥着重要作用.该文利用渐近分析工具,在正则性条件下研究了非凸多目标优化问题有效解集的非空性和有界性.首先,在正则条件下,建立了非凸多目标优化问题的有效解集和真有效解集的内外渐近估计;然后,根据这些估计,获得了非凸多目标优化问题有效解集的非空有界性的渐近刻画;最后,给出了非凸多目标优化问题有效解存在的必要条件.The non-emptiness and boundedness of the solution sets of optimization problems play a crucial role in numerical algorithms.Based on asymptotic analysis,the non-emptiness and boundedness of the(proper)efficient solution sets for nonconvex multi-objective optimization problems under regularity conditions were obtained.Firstly,the inner and outer asymptotic estimations were established for the efficient solution sets and the properly efficient solution sets of nonconvex multi-objective optimization problems via asymptotic cones and asymptotic functions.Then,based on these estimates,the non-emptiness and boundedness of the efficient solution sets for nonconvex multi-objective optimization problems were characterized.Finally,some necessary conditions for the existence of efficient solutions to nonconvex multi-objective optimization problem were given.

关 键 词：非凸多目标优化问题 有效解 正则性 渐近锥 渐近函数 

分 类 号：O221.6[理学—运筹学与控制论]