解含多个复杂分量函数无约束minimax问题的积极集光滑化算法  

An Active Set Smoothing Method for Solving UnconstrainedMinimax Problem with Multiple Complex ComponentFunctions

作　　者：周正勇[1] 秦丽娜 ZHOU Zhengyong;QIN Lina(School of Mathematics and Computer Science,Shanxi Normal University,Linfen 041004,China)

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041004

出　　处：《应用数学》2020年第3期690-698,共9页Mathematica Applicata

基　　金：国家自然科学基金(11701350)。

摘　　要：本文利用分段三次多项式方程构造了一种积极集策略的二次连续可微的光滑化max函数,给出积极集及稳定的光滑化max函数的计算方法.基于该光滑化max函数,结合Armijo线搜索,负梯度和牛顿方向及光滑化参数的更新策略,给出一种解含多个复杂分量函数无约束minimax问题的积极集光滑化算法.初步的数值实验表明了该算法的有效性.In this paper,a twice continuously differentiable active set smoothing maximum function is proposed,the smoothing maximum function is constructed by a piecewise cubic polynomial equation,and the stable strategies for computing the active set and the smoothing maximum function are given.Combining the active set smoothing maximum function,the Armijo line search,the steep descent direction and the Newton direction,and an update strategy for the smoothing parameters,an active set smoothing method is proposed for solving unconstrained minimax problems with multiple component functions.Preliminary numerical experiments show the efficiency of the proposed method.

关 键 词：MINIMAX问题 积极集 光滑化max函数 光滑化算法 

分 类 号：O224[理学—运筹学与控制论]