一般约束极大极小优化问题一个强收敛的广义梯度投影算法  

A Strongly Convergent Generalized Gradient Projection Method for Minimax Optimization with General Constraints

作　　者：马国栋 Ma Guodong(School of Mathematics and Statistics&Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,Yulin Normal University,Guangxi Yulin 537000)

机构地区：[1]玉林师范学院数学与统计学院&广西高校复杂系统优化与大数据处理重点实验室,广西玉林537000

出　　处：《数学物理学报（A辑）》2020年第3期641-649,共9页Acta Mathematica Scientia

基　　金：广西自然科学基金(2018GXNSFAA281099);国家自然科学基金(11771383);玉林师范学院科研项目(2019YJKY16,G20150010)。

摘　　要：该文考虑求解带非线性不等式和等式约束的极大极小优化问题,借助半罚函数思想,提出了一个新的广义投影算法.该算法具有以下特点:由一个广义梯度投影显式公式产生的搜索方向是可行下降的;构造了一个新型的最优识别控制函数;在适当的假设条件下具有全局收敛性和强收敛性.最后,通过初步的数值试验验证了算法的有效性.In this paper,minimax optimization problems with inequality and equality constraints is discussed.The original problem is transformed into an associated simple problem with a penalty term and only inequality constraints,then a new generalized gradient projection algorithm is presented.The main characters of the proposed algorithm are as follows:the improved search direction is generated by only one generalized gradient projection explicit formula;the new optimal identification function is introduced;the algorithm is globally and strongly convergent under some mild assumptions.Finally,the numerical results show that the proposed algorithm is promising.

关 键 词：非线性一般约束 极大极小问题 广义梯度投影算法 全局收敛性 强收敛性 

分 类 号：O221.2[理学—运筹学与控制论]