| 求解极大单调包含问题的一种新的近似邻近点算法 |
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| 引用本文： | 黄玲玲,刘三阳,高卫峰.求解极大单调包含问题的一种新的近似邻近点算法[J].兰州大学学报(自然科学版),2011,47(5):104-108. |
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| 作者姓名： | 黄玲玲 刘三阳 高卫峰 |
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| 作者单位： | 西安电子科技大学理学院,西安,710071 |
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| 基金项目： | 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) |
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| 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.
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| 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 |
A new approximate proximal point algorithm for maximal monotone inclusion problems |
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| HUANG Ling-ling,LIU San-yang,GAO Wei-feng.A new approximate proximal point algorithm for maximal monotone inclusion problems[J].Journal of Lanzhou University(Natural Science),2011,47(5):104-108. |
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| Authors: | HUANG Ling-ling LIU San-yang GAO Wei-feng |
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| Institution: | HUANG Ling-ling,LIU San-yang,GAO Wei-feng School of Science,Xidian University,Xi'an 710071,China |
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| Abstract: | 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. |
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| Keywords: | maximal monotone inclusion problem proximal point algorithm prediction-correction method global convergence |
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