Regularization Semismooth Newton Method for P0-NCPs with Non-monotone Line Search
Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear complementarity problem with a p0 -function. In this paper, we investigate the above algorithm with the monotone line search replaced by a non-mono...
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| Published in | Transactions of Tianjin University Vol. 16; no. 2; pp. 138 - 141 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Tianjin University
01.04.2010
School of Sciences, Tianjin University, Tianjin 300072, China%Tianjin University Beiyang Science and Technology Development Co. Ltd., Tianjin 300072, China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1006-4982 1995-8196 |
| DOI | 10.1007/s12209-010-0025-2 |
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| Abstract | Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear complementarity problem with a p0 -function. In this paper, we investigate the above algorithm with the monotone line search replaced by a non-monotone line search. It is shown that the non-monotone algorithm is well-defined, and is globally and locally superlinearly convergent under standard as- sumptions. |
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| AbstractList | O224; Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear complementarity problem with a P0-function. In this paper, we investigate the above algorithm with the monotone line search replaced by a non-monotone line search. It is shown that the non-monotone algorithm is well-defined, and is globally and locally superlinearly convergent under standard as-sumptions. Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear complementarity problem with a P 0 -function. In this paper, we investigate the above algorithm with the monotone line search replaced by a non-monotone line search. It is shown that the non-monotone algorithm is well-defined, and is globally and locally superlinearly convergent under standard assumptions. Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear complementarity problem with a p0 -function. In this paper, we investigate the above algorithm with the monotone line search replaced by a non-monotone line search. It is shown that the non-monotone algorithm is well-defined, and is globally and locally superlinearly convergent under standard as- sumptions. |
| Author | 王萍 臧玉卫 张颖 |
| AuthorAffiliation | School of Sciences, Tianjin University, Tianjin 300072, China Tianjin University Beiyang Science and Technology Development Co. Ltd., Yianjin 300072, China |
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| Copyright | Tianjin University and Springer Berlin Heidelberg 2010 Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | Fischer-Burmeister function semismooth Newton method nonlinearity complementarity |
| Language | English |
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| Notes | O221.2 12-1248/T nonlinearity complementarity semismooth Newton method nonlinearity; complementarity; semismooth Newton method; Fischer-Burrneister function Fischer-Burrneister function O242.23 |
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| Publisher | Tianjin University School of Sciences, Tianjin University, Tianjin 300072, China%Tianjin University Beiyang Science and Technology Development Co. Ltd., Tianjin 300072, China |
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| References | FacchineiF.PangJ. S.Finite-Dimensional Variational Inequalities and Complementarity Problems[M]2003New YorkSpringer Verlag ChenJ. S.PanS. H.A family of NCP functions and a descent method for the nonlinear complementarity problem[J]Computational Optimization and Applications20084033894041153.9054210.1007/s10589-007-9086-02411201 JiangH.QiL.A new nonsmooth equations approach to nonlinear complementarity problems[J]SIAM Journal on Control and Optimization19973511781930872.9009710.1137/S03630129942764941430288 ZhangH. C.HangerW. W.A nonmonotone line search technique and its application to unconstrained optimization[J]SIAM Journal on Optimization2004144104310561073.9002410.1137/S10526234034282082112963 FischerA.Solution of monotone complementarity problems with locally Lipschitzian functions[J]Mathematical Programming199776351353210.1007/BF026143961433969 SunD.A regularization Newton method for solving nonlinear complementarity problems[J]Applied Mathematics and Optimization19994033153390937.9011010.1007/s0024599001281709326 ChenJ. S.The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem[J]Journal of Global Optimization20063645655801144.9049310.1007/s10898-006-9027-y2269297 FacchineiF.KanzowC.Beyond monotonicity in regularization methods for nonlinear complementarity problems[J]SIAM Journal on Control and Optimization1999374115011610997.9008510.1137/S03630129973229351691935 FischerA.A special Newton-type optimization method[J]Optimization19922432692840814.6506310.1080/023319392088437951247636 ChenJ. S.PanS. H.A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P0-NCPs[J]Journal of Computational and Applied Mathematics20082201/24644791167.6503310.1016/j.cam.2007.08.0202444184 |
| References_xml | – reference: FischerA.Solution of monotone complementarity problems with locally Lipschitzian functions[J]Mathematical Programming199776351353210.1007/BF026143961433969 – reference: ChenJ. S.PanS. H.A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P0-NCPs[J]Journal of Computational and Applied Mathematics20082201/24644791167.6503310.1016/j.cam.2007.08.0202444184 – reference: FacchineiF.PangJ. S.Finite-Dimensional Variational Inequalities and Complementarity Problems[M]2003New YorkSpringer Verlag – reference: SunD.A regularization Newton method for solving nonlinear complementarity problems[J]Applied Mathematics and Optimization19994033153390937.9011010.1007/s0024599001281709326 – reference: FischerA.A special Newton-type optimization method[J]Optimization19922432692840814.6506310.1080/023319392088437951247636 – reference: ChenJ. S.PanS. H.A family of NCP functions and a descent method for the nonlinear complementarity problem[J]Computational Optimization and Applications20084033894041153.9054210.1007/s10589-007-9086-02411201 – reference: JiangH.QiL.A new nonsmooth equations approach to nonlinear complementarity problems[J]SIAM Journal on Control and Optimization19973511781930872.9009710.1137/S03630129942764941430288 – reference: FacchineiF.KanzowC.Beyond monotonicity in regularization methods for nonlinear complementarity problems[J]SIAM Journal on Control and Optimization1999374115011610997.9008510.1137/S03630129973229351691935 – reference: ZhangH. C.HangerW. W.A nonmonotone line search technique and its application to unconstrained optimization[J]SIAM Journal on Optimization2004144104310561073.9002410.1137/S10526234034282082112963 – reference: ChenJ. S.The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem[J]Journal of Global Optimization20063645655801144.9049310.1007/s10898-006-9027-y2269297 |
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| Snippet | Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear... Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear... O224; Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear... |
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| Title | Regularization Semismooth Newton Method for P0-NCPs with Non-monotone Line Search |
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