应用数学和力学2025，Vol.46Issue(4)：519-527,9.DOI:10.21656/1000-0887.450235
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
摘要
Abstract
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)ef-ficient solution sets for nonconvex multi-objective optimization problems under regularity conditions were ob-tained.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 solu-tion sets for nonconvex multi-objective optimization problems were characterized.Finally,some necessary con-ditions 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Key words
nonconvex multi-objective optimization/efficient solution/regularity/asymptotic cone/asymptot-ic function分类
数学引用本文复制引用
刘应,傅小恒,唐莉萍..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[J].应用数学和力学,2025,46(4):519-527,9.基金项目
国家自然科学基金(重大项目)(11991024) （重大项目）
国家自然科学基金(面上项目)(12171060) （面上项目）
重庆市自然科学基金(ncamc2022-msxm01 （）
CSTB2024NSCQ-LZX0140) （）
重庆市教委重大项目(KJZD-M202300504) 本文作者衷心感谢重庆师范大学博望学者青年拔尖人才项目和重庆师范大学启动基金项目(22XLB006)对本文的资助. （KJZD-M202300504）
