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
郑思情 1冯世强 1游曼雪1
作者信息
- 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
- 折叠
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.
Abstract
This paper obtains a dual problem for a general evenly convex optimization problem defined on a separat-ed 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 es-tablished 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Key words
evenly convex functions/C-conjugation/strong duality/stable strong duality/regularity conditions引用本文复制引用
基金项目
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)
西华师范大学校级资助项目(19B043)
西华师范大学创新创业项目(CXCY2023055)
出版年
2024
NETL
NSTL
万方数据