摘要
本文通过构造水平集辅助函数对一类积分全局最优性条件进行研究.所构造的辅助函数仅含有一个参数变量与一个控制变量,该参数变量用以表征对原问题目标函数最优值的估计,而控制变量用以控制积分型全局最优性条件的精度.对参数变量做极限运算即可得到积分型全局最优性条件.继而给出了用该辅助函数所刻画的全局最优性的充要条件,从而将原全局优化问题的求解转化为寻找一个非线性方程根的问题.更进一步地,若所取测度为勒贝格测度且积分区域为自然数集合的一个有限子集,则该积分最优性条件便化为有限极大极小问题中利用凝聚函数对极大值函数进行逼近的近似系统.从而积分型全局最优性条件可以看作是该近似系统从离散到连续的一种推广.
An integral optimality condition for global optimization problem is investigated by using a level set auxiliary function.The auxiliary function has one variant that represents an estimated optimal value of the objective function in primal optimization problem and one controlling parameter for accuracy.Necessary and sufficient condition for global optimality in terms of the behavior of the auxiliary function is derived.The integral global optimality condition is obtained via a limiting process of this auxiliary function.Furthermore,if the measure is the Lebesgue measure and the integral region takes a finite subset of the Natural Number set,then this integral global optimality condition divergences to the approximation scheme that used aggregate function to approximate the max-function in the finite minimax problem.So the integral global optimality condition is an extension of this approximation scheme in continuous maximum problem.
出处
《运筹学学报》
CSCD
2011年第1期1-10,共10页
Operations Research Transactions
基金
supported by the National Natural Science Foundation of China(No.10902077)
关键词
运筹学
积分型最优性条件
水平集
勒贝格测度
全局优化
凝聚函数
Operations research
integral optimality condition
level set
Lebesque measure
global optimization
aggregate function
