求解大规模极大极小问题的光滑化三项共轭梯度算法  

A SMOOTHING THREE-TERM CONJUGATE GRADIENT METHOD FOR SOLVING FINITE MINIMAX PROBLEMS

作　　者：郭洁 万中[2] Guo Jie;Wan Zhong(School of Mathematical Sciences,ChangSha Normal University,ChangSha 410100,China;School of Mathematics and Statistics,Central South University,ChangSha,410083,China)

机构地区：[1]长沙师范学院数学科学学院,长沙410100 [2]中南大学数学与统计学院,长沙410083

出　　处：《计算数学》2022年第3期324-338,共15页Mathematica Numerica Sinica

基　　金：国家社会科学基金项目(21BGL122);国家自然科学基金项目(71671190)资助。

摘　　要：基于指数罚函数,对最近提出的一种求解无约束优化问题的三项共轭梯度法进行了修正,并用它求解更复杂的大规模极大极小值问题.证明了该方法生成的搜索方向对每一个光滑子问题是充分下降方向,而且与所用的线搜索规则无关.以此为基础,设计了求解大规模极大极小值问题的算法,并在合理的假设下,证明了算法的全局收敛性.数值实验表明,该算法优于文献中已有的类似算法.In this paper,by the method of exponential penalty,we modify the recently proposed three-term conjugate gradient method for solving optimization problems such that it is used to solve more complicated large-scale minimax problems.It is proved that the search directions generated by our method are sufficiently descent for the smoothing subproblems,being independent of the used line search rules.With such a property,a new algorithm is developed to solve the large-scale min-max problems,and its global convergence is established under mild assumptions.By numerical experiments,it is shown that this algorithm outperforms the other similar ones available in the literature.

关 键 词：极大极小问题 光滑化方法 共轭梯度法 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]