A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems
We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton meth...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/560578 |
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| _version_ | 1832564754985517056 |
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| author | Yuan Li Hai-Shan Han Dan-Dan Yang |
| author_facet | Yuan Li Hai-Shan Han Dan-Dan Yang |
| author_sort | Yuan Li |
| collection | DOAJ |
| description | We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient. |
| format | Article |
| id | doaj-art-6e1b4ea1d1584be491564fd722705980 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6e1b4ea1d1584be491564fd7227059802025-02-03T01:10:14ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/560578560578A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity ProblemsYuan Li0Hai-Shan Han1Dan-Dan Yang2College of Mathematics, Inner Mongolia University for the Nationalities, The Inner Mongolia Autonomous Region, Tongliao 028000, ChinaCollege of Mathematics, Inner Mongolia University for the Nationalities, The Inner Mongolia Autonomous Region, Tongliao 028000, ChinaCollege of Mathematics, Inner Mongolia University for the Nationalities, The Inner Mongolia Autonomous Region, Tongliao 028000, ChinaWe consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient.http://dx.doi.org/10.1155/2014/560578 |
| spellingShingle | Yuan Li Hai-Shan Han Dan-Dan Yang A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems Journal of Mathematics |
| title | A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems |
| title_full | A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems |
| title_fullStr | A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems |
| title_full_unstemmed | A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems |
| title_short | A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems |
| title_sort | penalized equation based generalized newton method for solving absolute value linear complementarity problems |
| url | http://dx.doi.org/10.1155/2014/560578 |
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