一种新的求总极值的水平值估计算法  

A new level-value estimation method for global minimization

作　　者：楼烨[1,2] 孙胜[2] 武明楠[2] 

机构地区：[1]上海科学技术职业学院,上海201800 [2]上海大学理学院,上海200444

出　　处：《运筹学学报》2012年第2期105-114,共10页Operations Research Transactions

摘　　要：提出了一种求解总极值问题的新水平值估计算法.为此,引入一类变差函数并研究它的性质;给出基于变差函数的全局最优性条件,并构造出一种求总极值的水平值估计算法.为了实现这种算法,采用了基于重点样本技术的Monte-Carlo方法来计算变差,并利用相对熵算法的主要思想更新取样密度.初步的数值实验说明了算法的有效性.In this paper,a new level-value estimation method is proposed for solving global optimization problem.For this purpose,we introduce a deviation function and study its properties.Based the deviation function,we give a global optimality condition, and then propose a conceptual level-value estimation algorithm,and prove the global convergence of the proposed method.For the implementation of the proposed method, we use the Monte-Carlo method with important sampling to compute the deviation,in which the sample density is updated by the main ideas of the cross-entropy method.Some primary numerical results show the validity of the proposed method.

关 键 词：总极值 变差函数 水平值估计算法 重点取样 相对熵算法 

分 类 号：O221.2[理学—运筹学与控制论]