关于数学期望型水平值逼近优化问题总极值的算法  

On Mathematical Expectation of Level Value Approximating to Global Minimum of a Class Optimization Problem

作　　者：彭拯[1] 邬冬华[2] 杨毅[2] 

机构地区：[1]南京大学数学系,南京210093 [2]上海大学数学系,上海200444

出　　处：《运筹学学报》2008年第3期121-128,共8页Operations Research Transactions

基　　金：国家自然科学基金(NSFC10671117);湖南教育厅青年项目(06B037)资助

摘　　要：本文研究用数学期望型水平值逼近一类优化问题总极值的算法,证明了算法所构造的数学期望型水平值迭代方程的解的存在唯一性,同时证明了方程的解是原来优化问题的总极值,并对可统一到该算法理论框架下的几种可实现算法进行了简要描述,数值实验结果验证了算法的有效性.In this paper, we investigate the method which use mathematical expectation of level value to approximate to the global minimum of a class optimization problem. We prove the existence and uniqueness of the solution of the mathematical expectation iteration equation, and also prove that the unique solution of this equation is just the global minimum of the original optimization problem. Furthermore, we give a brief presentation on some implementable algorithms, which can be felled under the concept algorithm that use mathematical expectation of level value to approximate to the global minimum, the results of numerical tests show the efficient of those algorihtms.

关 键 词：运筹学 总极值 数学期望型水平值迭代方程 解的存在唯一性 等价性 

分 类 号：O224[理学—运筹学与控制论] TP301.6[理学—数学]