| 求解凸不等式问题的熵光滑化方法 |
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| 引用本文： | 李兴斯,张培爱.求解凸不等式问题的熵光滑化方法[J].高等学校计算数学学报,2004,26(1):25-29. |
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| 作者姓名： | 李兴斯 张培爱 |
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| 作者单位： | 1. 大连理工大学力学系,大连,116024
2. 暨南大学数学系,广州,510632 |
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| 基金项目： | 基础性研究专项基金(G1999032805) |
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| 摘 要： | The maximal entropy principle is applied to solve convex inequality problems. An inequality problem can be transformed into a minmax problem.Then it can be transformed into an unconstrained parameterized min problem,using the entropic function to smooth the minmax problem. The solution of the inequality problem can be obtained, by solving the parameterized min problems and adjusting the parameter to zero, under a certain principle. However, it is sufficient to solve a parameterized inequality problem each time, from the propositions of the aggregate function. In the article, some propositions of the aggregate function are discussed, the algorithm and its convergence are obtained.
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| 关 键 词： | 凸不等式 熵光滑化 凸函数 Shannon熵函数 Lagrange函数 极大极小问题 |
AN ENTROPIC SMOOTHING METHOD FOR SOLVING CONVEX INEQUALITY PROBLEMS |
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| Li Xingsi.AN ENTROPIC SMOOTHING METHOD FOR SOLVING CONVEX INEQUALITY PROBLEMS[J].Numerical Mathematics A Journal of Chinese Universities,2004,26(1):25-29. |
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| Authors: | Li Xingsi |
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| Abstract: | The maximal entropy principle is applied to solve convex inequality problems. An inequality problem can be transformed into a minmax problem. Then it can be transformed into an unconstrained parameterized min problem, using the entropic function to smooth the minmax problem. The solution of the inequality problem can be obtained, by solving the parameterized min problems and adjusting the parameter to zero, under a certain principle. However, it is sufficient to solve a parameterized inequality problem each time, from the propositions of the aggregate function. In the article, some propositions of the aggregate function are discussed, the algorithm and its convergence are obtained. |
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| Keywords: | inequality problem aggregate function convergence |
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