| 一种无约束全局优化的水平值下降算法 |
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| 引用本文： | 彭拯,张海东,邬冬华. 一种无约束全局优化的水平值下降算法[J]. 应用数学, 2007, 20(1): 213-219 |
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| 作者姓名： | 彭拯 张海东 邬冬华 |
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| 作者单位： | 1. 湖南理工学院数学系,湖南,岳阳,414006;上海大学数学系,上海,200444
2. 上海大学数学系,上海,200444 |
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| 基金项目： | 上海市重点学科建设项目;湖南省教育厅科研项目 |
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| 摘 要： | 本文研究无约束全局优化问题,建立了一种新的水平值下降算法(Level-value Descent Method,LDM).讨论并建立了概率意义下取全局最小值的一个充分必要条件,证明了算法LDM是依概率测度收敛的.这种LDM算法是基于重点度取样(Improtance Sampling)和Markov链Monte-Carlo随机模拟实现的,并利用相对熵方法(TheCross-Entropy Method)自动更新取样密度,算例表明LDM算法具有较高的数值精度和较好的全局收敛性.
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| 关 键 词： | 全局最优化 水平值下降算法 随机实现 相对熵方法 |
| 文章编号： | 1001-9847(2007)01-0213-07 |
| 修稿时间： | 2006-06-30 |
A Level Value Descent Method for Unconstrained Global Optimization Problems |
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| PENG Zheng,ZHANG Hai-dong,WU Dong-hua. A Level Value Descent Method for Unconstrained Global Optimization Problems[J]. Mathematica Applicata, 2007, 20(1): 213-219 |
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| Authors: | PENG Zheng ZHANG Hai-dong WU Dong-hua |
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| Affiliation: | 1. Department of Mathematics, Hunan Institute of Technology and Science, Yueyang 414006, China 2. Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| Abstract: | We propose a level value descent method for unconstrained global optimization problem in this paper.Discuss and establish a sufficient and necessary condition for the global optimum in probability measure,and prove that the LDM algorithm is convergence in probability.The implementation of the LDM algorithm is based on importance sampling and Markov Chain Monte-Carlo,and update the probability density function by the cross-entropy method.The numerical results show it has a better operational precision and global convergent. |
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| Keywords: | Global optimization The level-value descent method Stochastic implementation The cross-entropy method |
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