广义半无限规划新的最优性条件(英文)  

New Optimality Conditions for Generalized Semi-Infinite Min-Max Programming

作　　者：周金川 王长钰 刘丙状 李梅霞 

机构地区：[1]Department of Mathematics,School of Science,Beijing Jiaotong University,Beijing100044,China [2]Institute of Operations Research,Qufu Normal University,Qufu 273165,China [3]School of Science,Shandong University of Technology,Zibo 255049,China [4]School of Mathematics and Information Science,Weifang University,Shandong261061,China

出　　处：《运筹学学报》2009年第1期1-14,共14页Operations Research Transactions

基　　金：supported by the National Natural Science Foundation of China(10571106,70871008,10701047).

摘　　要：本文讨论了一类指标集依赖于决策变量的广义半无限规划(GSMMP).首先通过刻画目标函数的Clarke导数和Clarke次微分,建立其一阶最优性条件.其次,通过对下层问题Q(X)进行扰动分析,我们得到Q(X)的一个精确罚表示.由此,利用一组精确罚函数将(GSMMP)转化为经典的半无限极大极小规划,从而可利用已有的经典半无限规划的算法来对(GSMMP)进行求解.This paper deals with a class of generalized semi-infinite min-max programming （GSMMP）, in which the index set depends on the decision variable. Based on some new characterizations of the Clarke derivative and Clarke subdifferential of the objective function, we develop the first-order optimality conditions for （GSMMP） in terms of second-order multipliers. Moreover, by addressing the perturbed problem of the lowerlevel programming Q（x）, we obtain an exact penalty representations for Q（x）, which allows us to convert （GSMMP） into the standard semi-infinite min-max programming via a class of exact penalty functions. This fact makes it possible to solve （GSMMP） by using any available standard semi-infinite optimization algorithms.

关 键 词：运筹学 广义半无限极大极小规划 罚函数 一阶最优性条件 

分 类 号：O221[理学—运筹学与控制论] O224[理学—数学]