| 熵正则化方法与指数(乘子)罚函数法之间的关系 |
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| 引用本文： | 姜昱汐,潘少华,李兴斯.熵正则化方法与指数(乘子)罚函数法之间的关系[J].高等学校计算数学学报,2005,27(4):355-362. |
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| 作者姓名： | 姜昱汐 潘少华 李兴斯 |
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| 作者单位： | 大连理工大学应用数学系,大连,116024;华南理工大学数学科学学院,广州,510641;大连理工大学工业装备结构分析国家重点实验室,大连,116024 |
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| 摘 要： | 由于极大极小问题在许多科学与工程中有着重要应用，特别是形如max的函数频繁地出现在各类数值分析和优化问题中，因此对于求解该类问题的算法研究长久不衰，这些算法一般分为两大类：一类是直接法，其算法设计仅以有效地求解原问题（P）为目的；另一类是间接法，其算法以找一个能够替代不可微max函数φ（x）的光滑函数为目的，故这类算法被称为光滑化方法，文1，2]中的熵正则化方法就属于光滑化方法范畴。
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| 关 键 词： | 正则化方法 罚函数法 算法研究 乘子 指数 极大极小问题 熵 优化问题 数值分析 算法设计 |
| 收稿时间： | 02 8 2004 12:00AM |
| 修稿时间： | 2004-02-08 |
RELATIONSHIP BETWEEN ENTROPY REGULARIZATION METHOD AND EXPONENTIAL PENALTY METHOD |
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| Jiang Yuxi,Pan Shaohua,Li Xingsi.RELATIONSHIP BETWEEN ENTROPY REGULARIZATION METHOD AND EXPONENTIAL PENALTY METHOD[J].Numerical Mathematics A Journal of Chinese Universities,2005,27(4):355-362. |
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| Authors: | Jiang Yuxi Pan Shaohua Li Xingsi |
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| Institution: | 1.Department of Applied Mathematics, Dalian University of Technology, Dalian 116024; 2.School of Mathematics Sciences, South China University of Technology, Guangzhou 510641; 3.State Key Lab. of Structural Anaiysis for Industrial Equipment, Dalian University of Technology, Dalian 116024 |
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| Abstract: | In papers, two smooth functions uniformly approximating the max-type function were derived for the finite min-max problem through an entropy regularization method. Here, we present an alternative derivation of these smooth functions by means of the conventional exponential (multiplier) penalty method, whereby exploring a duality relationship between these two approaches. We also give a rigorous proof for this duality property with use of the Fenchel duality theorem in convex analysis. It is hoped that this paper would help correct understanding of the entropy regularization method and proper use of corresponding sinooth functions. |
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| Keywords: | finite rain-max problem entropy regularization method exponentialpenalty method duality relationship |
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