一种新的求解带约束的有限极大极小问题的精确罚函数  

A New Exact Penalty Function for Solving Constrained Finite Min-Max Problems

作　　者：马骋[1] 李迅[1] 姚家晖[1] 张连生[2] 

机构地区：[1]香港理工大学应用数学系 [2]上海大学数学系,上海200444

出　　处：《应用数学和力学》2012年第2期250-264,共15页Applied Mathematics and Mechanics

基　　金：AMSS-PolyU联合研究所资助项目

摘　　要：提出了一种新的精确光滑罚函数求解带约束的极大极小问题.仅仅添加一个额外的变量,利用这个精确光滑罚函数,将带约束的极大极小问题转化为无约束优化问题.证明了在合理的假设条件下,当罚参数充分大,罚问题的极小值点就是原问题的极小值点.进一步,研究了局部精确性质.数值结果表明这种罚函数算法是求解带约束有限极大极小问题的一种有效算法.A new exact yet smooth penalty function to tackle constrained min-max problems was introduced. Using this new penalty function and adding just one extra variable, a con- strained min-max problem was transformed into an unconstrained optimization one. It was proved that, under certain reasonable assumptions and when the penalty parameter was suffi- ciently large, the minimizer of this unconstrained optimization problem was equivalent to the minimizer of the original constrained one. Moreover, the local exactness property was also studied. The numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.

关 键 词：带约束的极大极小问题 约束优化问题 罚函数 

分 类 号：O221.2[理学—运筹学与控制论]