PPA BASED PREDICTION-CORRECTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES
In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a...
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| Veröffentlicht in: | 高等学校计算数学学报（英文版） 2005, Vol.14 (1), p.14-30 |
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| container_title | 高等学校计算数学学报（英文版） |
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| creator | 何炳生 蒋建林 钱迈建 许娅 |
| description | In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions. |
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In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.</description><identifier>ISSN: 1004-8979</identifier><identifier>EISSN: 2079-7338</identifier><language>eng</language><publisher>Department of Mathematics, Nanjing University, Nanjing 210093, PRC%Department of Mathematics, California State University, Fullerton, CA92834, USA</publisher><subject>不等式 ; 最接近点计算法 ; 计算方法 ; 预测方法</subject><ispartof>高等学校计算数学学报（英文版）, 2005, Vol.14 (1), p.14-30</ispartof><rights>Copyright © Wanfang Data Co. Ltd. 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We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. 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| identifier | ISSN: 1004-8979 |
| ispartof | 高等学校计算数学学报（英文版）, 2005, Vol.14 (1), p.14-30 |
| issn | 1004-8979 2079-7338 |
| language | eng |
| recordid | cdi_wanfang_journals_gdxxjssxxb_e200501002 |
| source | Alma/SFX Local Collection |
| subjects | 不等式 最接近点计算法 计算方法 预测方法 |
| title | PPA BASED PREDICTION-CORRECTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES |
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