求解极大单调包含问题的一种新的近似邻近点算法  

A new approximate proximal point algorithm for maximal monotone inclusion problems

作　　者：黄玲玲[1] 刘三阳[1] 高卫峰[1] 

机构地区：[1]西安电子科技大学理学院,西安710071

出　　处：《兰州大学学报（自然科学版）》2011年第5期104-108,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(60974082);国家重点实验室专项基金项目(ISN02080003);中央高校基本科研业务费专项资金项目(JY10000970006)

摘　　要：采用经典的非精确邻近点算法作为预测步,并采用当前迭代点的一个凸组合作为校正步,提出了一种新的用于求解极大单调包含问题的近似邻近点算法.在仅要求解集非空的前提下,证明了新算法具有全局收敛性.一些现有算法可以看作是新算法的特殊情形.A new approximate proximal point algorithm for maximal monotone inclusions was proposed. Each iteration of the new algorithm consisted of two steps： a prediction and a correction. The predictor was produced by an inexact proximal point algorithm; and then it was corrected by a convex combination of the current iteration. Global convergence of the new algorithm was proved provided that the solution set was nonempty. Furthermore, some existing algorithms can be considered as the special cases of the new algorithm.

关 键 词：极大单调包含问题 邻近点算法 预测校正算法 全局收敛 

分 类 号：O221.2[理学—运筹学与控制论]