| 复合凸优化问题全对偶性的等价刻画 |
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| 引用本文： | 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(1):33-36. |
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| 作者姓名： | 孙祥凯 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金，中国博士后科学基金，重庆市基础与前沿研究计划项目 |
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| 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.
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| 关 键 词： | 复合凸优化问题 Moreau Rockafellar法则 稳定全对偶 全对偶 |
| 收稿时间： | 2014-04-08 |
Some Characterizations of Total Duality for a Composed Convex Optimization |
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| SUN Xiangkai.Some Characterizations of Total Duality for a Composed Convex Optimization[J].Journal of Jilin University: Sci Ed,2015,53(1):33-36. |
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| Authors: | SUN Xiangkai |
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| Institution: | 1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;[JP]2. College of Automation, Chongqing University, Chongqing 400030, China |
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| 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. |
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| Keywords: | composed convex optimization problem Moreau-Rockafellar formula stable total duality total duality |
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