复合凸优化问题全对偶性的等价刻画

吉林大学学报(理学版)

复合凸优化问题全对偶性的等价刻画

孙祥凯

1. 重庆工商大学数学与统计学院, 重庆 400067; 2. 重庆大学自动化学院, 重庆 400030

收稿日期:2014-04-08 出版日期:2015-01-26 发布日期:2015-01-19
通讯作者: 孙祥凯 E-mail:sxkcqu@163.com

Some Characterizations of Total Duality for a Composed Convex Optimization

SUN Xiangkai

1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;[JP]2. College of Automation, Chongqing University, Chongqing 400030, China

Received:2014-04-08 Online:2015-01-26 Published:2015-01-19
Contact: SUN Xiangkai E-mail:sxkcqu@163.com

摘要/Abstract

摘要：

先建立一类复合凸优化问题的对偶问题, 再利用次微分性质引入关于复合凸函数的一类新的MoreauRockafellar法则, 等价刻画了该复合凸优化问题的稳定全对偶及全对偶.

关键词: 复合凸优化问题, MoreauRockafellar法则, 稳定全对偶, 全对偶

Abstract:

We first introduced the dual schemes for a composed convex optimization problem. Then, using the properties of subdifferential, we introduced a new MoreauRockafellar formula for a composed convex function. And using the MoreauRockafellar formula, we obtained some necessary and sufficient conditions which characterize the stable total duality for the composed convex optimization problem.

Key words: composed convex optimization problem, MoreauRockafellar formula, stable total duality, total duality

中图分类号:

O221.6

孙祥凯. 复合凸优化问题全对偶性的等价刻画[J]. 吉林大学学报(理学版), 2015, 53(01): 33-36.

SUN Xiangkai. Some Characterizations of Total Duality for a Composed Convex Optimization[J]. Journal of Jilin University Science Edition, 2015, 53(01): 33-36.