| 数学期望型水平值逼近全局最小值的方法 |
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| 引用本文： | 陈安亮,楼烨. 数学期望型水平值逼近全局最小值的方法[J]. 应用数学与计算数学学报, 2010, 24(2): 67-74 |
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| 作者姓名： | 陈安亮 楼烨 |
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| 作者单位： | [1]上海大学理学院数学系,上海200444 [2]上海科学技术职业学院,上海201800 |
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| 基金项目： | 上海自然科学基金课题，上海市教委科技创新重点项目 |
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| 摘 要： | 郑权在1978年提出的一种积分水平集算法概念性算法.由于水平集一般情况下难以求出,此算法通过Monte-Carlo随机取点来实现.本文提出了数学期望型水平值逼近全局最小值的概念性算法,它利用了相对熵主要思想,通过改变重要样本密度函数,克服了郑权算法水平集不易求得而难以求出水平值的困难.本文还给出了求全局最小值的收敛准则并证明了它的渐进收敛性.
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| 关 键 词： | 积分水平集 相对熵 重要样本 kullback-leibler距离 |
Mathematical Expectation Method of Level approximating to Global Minimum |
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| Chen Anliang,Lou Ye. Mathematical Expectation Method of Level approximating to Global Minimum[J]. Communication on Applied Mathematics and Computation, 2010, 24(2): 67-74 |
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| Authors: | Chen Anliang Lou Ye |
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| Affiliation: | Chen Anliang Lou Ye Department of Mathematics,Shanghai University,Shanghai 200444 Shanghai Professional College of Science and Technology, Shanghai 201800,China |
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| Abstract: | Zheng Quan proposed a conceptual algorithm of integral global optimization in 1978.This algorithm is implementable approach by Monte-Carlo method because the level set is difficult to solve.This paper presents a conceptual algorithm of mathematical expectation of level value approximating to global minimum that uses the main idea of the cross-entropy method and avoids solving level set procedure by changing the important sample probability density function.This paper also gives convergence criterion of global minimum for the new conceptual algorithm and proves its asymptotic convergence. |
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| Keywords: | integral-level set cross-entropy important sample kullback-leibler distance |
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