一类DC复合优化问题的Fenchel C-conjugate对偶理论  

Fenchel C-conjugate dual theory for a class of DC composite optimization problems

作　　者：魏俊林 游曼雪 WEI Junlin;YOU Manxue(School of Mathematic and Information,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《内江师范学院学报》2024年第8期28-34,共7页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(12001438);西华师范大学校级资助项目(18Q059,19B043)。

摘　　要：在局部分离凸空间中,考虑无约束的DC复合优化问题.根据均匀凸(简称e-凸)函数在c-共轭框架下的Fenchel-Moreau定理,利用扰动方法建立了DC复合优化问题的Fenchel对偶问题.进一步,借助c-共轭函数的上图性质,给出了原问题与Fenchel对偶问题的零对偶间隙,弱对偶和强对偶成立的正则条件.In the locally separated convex space,the unconstrained DC composite optimization problems is considered.According to the Fenchel-Moreau theorem of evenly convex(e-convex,in brief)function in the c-conjugate scheme,the Fenchel duality problem of DC composite optimization problem is established by perturbation method.Furthermore,by means of the properties of the epigraph of the c-conjugate function,the regularity conditions for the zero duality gap,the weak duality,and the strong duality of the primal problem and Fenchel duality problem are given.

关 键 词：DC复合优化 均匀凸函数 c-共轭框架 Fenchel对偶 正则条件 

分 类 号：O224[理学—运筹学与控制论]