积分总极值方法在有界可测函数上的推广  

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

作　　者：朱环宇[1] 邬冬华[1] 黄文杰[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《上海大学学报（自然科学版）》2007年第1期47-50,54,共5页Journal of Shanghai University:Natural Science Edition

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,1999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.An integral-level set method for solving global optimization problems was proposed in 1978 and improved in 1999 .This method has only been used in continuous functions in a closed domain. In this paper, the method is extended to bounded measurable 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.

关 键 词：总极值 积分 水平集 有界可测函数 最优性条件 

分 类 号：O221.2[理学—运筹学与控制论]