广义半无限极大极小规划的一个新的最优性条件  

A New Optimality Condition on Generalized Semi-infinite Min-max Problems

作　　者：刘茜[1] 

机构地区：[1]山东师范大学数学科学学院,济南250014

出　　处：《重庆师范大学学报（自然科学版）》2009年第2期12-17,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10826031;No.10571106;No.10771228);运筹学与系统工程重庆市市级重点实验室开放课题(No.2006001)

摘　　要：由于广义半无限极大极小问题的极大函数的约束集合随x的变化而变化,增加了对该问题的理论分析和求解难度。为了克服这种情况,许多研究者考虑通过转化消除约束集合中的约束f(x,y)≤0。本文是通过一类由1范数定义的精确罚,将广义的半无限极大极小规划中的约束条件消除,使该问题转化为半无限极小极大极小规划。在不需要假设集合的条件下证明,当罚参数充分大时,半无限极小极大极小规划与广义半无限极大极小问题具有相同的最优值,相同的局部最优解以及相同的全局最优解。利用这种等价性,进一步给出了广义半无限极大极小问题的一个最优性条件。最后,对本文中建立的最优性条件与其它文献中的最优性条件之间的关系进行了讨论。Generalized semi-infinite min-max problem has important relations with optimal control and information technology. It can be used in various engineering fields. So it is very interesting to study the generalized semi-infinite min-max problem. However, since the constraint set change as the variable x changes, the generalized semi-infinite rain-max problem is difficult to be solved. To overcome these difficulties, investigators have developed many important progresses of generalized semi-infinite min-max programs. In this paper, we use 11 exact penalty function to remove the constraint conditions of a generalized semi-infinite min-max problem, and then convert this problem into a semi-infinite min-max-min problem. Without the compactness assumption, we prove that the generalized semi-infinite rain-max problem has the same optimal value, the same set of local and global solutions as the corresponding semi-infinite min- max-min problem, when the penalty parameter is sufficiently large. Using these results, we give an optimality condition for the generalized semi-infinite rain-max problem. Furthermore, we discuss the relations between the optimality condition given in this paper and other existing optimality conditions.

关 键 词：半无限优化 非光滑优化 精确罚 

分 类 号：O224[理学—运筹学与控制论] O221.2[理学—数学]