井冈山大学学报（自然科学版）2024，Vol.45Issue(2)：12-20,9.DOI:10.3969/j.issn.1674-8085.2024.02.003
DC复合优化问题的两种Fenchel对偶模型研究
RESEARCH ON TWO FENCHEL DUAL MODELS FOR DC COMPOSITE OPTIMIZATION PROBLEMS
摘要
Abstract
The model considered in this paper is an unconstrained DC composite convex optimization problem.Firstly,two Fenchel duality problems for DC composite optimization problems are established by using perturbation method,generalized convex conjugation theorem under c-conjugate scheme and evenly convex(e-convex,in brief)technique.Secondly,three important sets are given by using the properties of the epigraph of the c-conjugate function.Finally,the strong duality of two pairs of primal-dual problems and the equivalence between them are described under the assumption of e-convex function.关键词
DC复合凸优化/c-共轭框架/Fenchel对偶/均匀凸函数Key words
DC composite optimization/c-conjugate scheme/Fenchel duality/evenly convex function分类
数理科学引用本文复制引用
魏俊林,游曼雪..DC复合优化问题的两种Fenchel对偶模型研究[J].井冈山大学学报（自然科学版）,2024,45(2):12-20,9.基金项目
国家自然科学基金项目(12001438) （12001438）
西华师范大学校级项目(18Q059,19B043) （18Q059,19B043）
