积分总极值方法在有界可测函数上的推广

上海大学学报(自然科学版)

积分总极值方法在有界可测函数上的推广

朱环宇;邬冬华;黄文杰

上海大学理学院,上海 200444

收稿日期:2006-03-08 出版日期:2007-02-28 发布日期:2007-02-28

Extension of Integral Level Set Method for Global Optimization to Bounded Measurable Functions

ZHU Huan yu;WU Dong hua;HUANG Wen jie

School of Sciences, Shanghai University, Shanghai 200444, China

Received:2006-03-08 Online:2007-02-28 Published:2007-02-28

摘要/Abstract

摘要： 1978年，郑权等提出了积分型求总极值的方法来解决求解全局最优解的问题，19 99年，邬冬华等对原郑权的方法作了一些改进，提出了修正的积分型求总极值方法.然而到目前为止，积分总极值方法还仅限于定义域为闭集的连续函数.利用本质下确界的概念以及勒贝格积分的特性，将积分总极值方法推广到了有界可测函数上，提出了针对有界可测函数的理论算法，并给出了其最优性条件.

关键词: 积分水平集, 有界可测函数, 总极值, 最优性条件

Abstract: An integral level set method for solving global optimization problems was propo sed in 1978 and improved in 1999.This method has only been used in continuous fu nctions in a closed domain.In this paper,the method is extended to bounded measu r able functions by introducing the concept of essential infimum and the property of Lebesgue integral.An integral level set conceptual algorithm is proposed for bounded measurable functions,and an optimality condition is obtained.

Key words: bounded mea surable functions, integral level set, optimality condition , global optimization

朱环宇;邬冬华;黄文杰. 积分总极值方法在有界可测函数上的推广[J]. 上海大学学报(自然科学版).

ZHU Huan yu;WU Dong hua;HUANG Wen jie . Extension of Integral Level Set Method for Global Optimization to Bounded Measurable Functions[J]. Journal of Shanghai University（Natural Science Edition）.

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