一般复合均匀凸优化的强和稳定对偶  

Strong and Stable Duality of General Composed Evenly Convex Optimization

作　　者：郑思情 冯世强[1] 游曼雪 ZHENG Siqing;FENG Shiqiang;YOU Manxue(Mathematics and Information School of China West Normal University,Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院&最优化理论与应用四川省高校重点实验室,四川南充637009

出　　处：《四川文理学院学报》2024年第2期56-66,共11页Sichuan University of Arts and Science Journal

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);西华师范大学创新创业项目(CXCY2023055)。

摘　　要：在广义凸共轭理论的基础和可分离的局部凸空间的条件下,利用扰动方法和c—共轭方法得到一般复合均匀凸优化问题的对偶问题,并在原问题的基础上再扰动一个连续线性泛函得到其稳定对偶问题.进而在一定的假设条件下,结合函数的均匀凸性,给出保证强对偶和稳定强对偶成立的正则条件.This paper obtains a dual problem for a general evenly convex optimization problem defined on a separated locally convex space,via perturbational approach and using a conjugation scheme called c-conjugation.This scheme is based on the generalized convex conjugation theory.Regularity conditions guaranteeing strong duality for primal problems which are perpetuated by continuous linear functional and its dual problems,which is named stable strong duality,are established under certain assumptions,where the evenly convexity of the perturbation function plays a fundamental role.

关 键 词：均匀凸函数 c-共轭 强对偶 稳定强对偶 正则条件 

分 类 号：O224[理学—运筹学与控制论]