Convergence rate analysis of an asynchronous space decomposition method for convex minimization
We analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive Banach space. This method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations. In par...
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sg-ntu-dr.10356-907542023-02-28T19:24:16Z Convergence rate analysis of an asynchronous space decomposition method for convex minimization Tai, Xue Cheng Tseng, Paul School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis We analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive Banach space. This method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations. In particular, the method generalizes the additive Schwarz domain decomposition methods to allow for asynchronous updates. It also generalizes the BPX multigrid method to allow for use as solvers instead of as preconditioners, possibly with asynchronous updates, and is applicable to nonlinear problems. Applications to an overlapping domain decomposition for obstacle problems are also studied. The method of this work is also closely related to relaxation methods for nonlinear network flow. Accordingly, we specialize our convergence rate results to the above methods. The asynchronous method is implementable in a multiprocessor system, allowing for communication and computation delays among the processors. Published version 2009-08-12T02:54:16Z 2019-12-06T17:53:22Z 2009-08-12T02:54:16Z 2019-12-06T17:53:22Z 2001 2001 Journal Article Tai, X. C., & Tseng, P. (2001). Convergence rate analysis of an asynchronous space decomposition method for convex minimization. Mathematics of Computation, 71(239), 1105-1135. 0025-5718 https://hdl.handle.net/10356/90754 http://hdl.handle.net/10220/6054 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2002&volume=71&issue=239&spage=1105&epage=1135&aulast=Tai&aufirst=%20X%20%2DC&auinit=&title=Mathematics%20of%20Computation&atitle=Convergence%20rate%20analysis%20of%20an%20asynchronous%20space%20decomposition%20method%20for%20convex%20minimization&sici. 10.1090/S0025-5718-01-01344-8. en Mathematics of computation. Mathematics of Computation © copyright 2001 American Mathematical Society. The journal's website is located at http://www.ams.org/mcom/. 31 p. application/pdf |
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DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis Tai, Xue Cheng Tseng, Paul Convergence rate analysis of an asynchronous space decomposition method for convex minimization |
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We analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive Banach space. This method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations. In particular, the method generalizes the additive Schwarz domain decomposition methods to allow for asynchronous updates. It also generalizes the BPX multigrid method to allow for use as solvers instead of as preconditioners, possibly with asynchronous updates, and is applicable to nonlinear problems. Applications to an overlapping domain decomposition for obstacle problems are also studied. The method of this work is also closely related to relaxation methods for nonlinear network flow. Accordingly, we specialize our convergence rate results to the above methods. The asynchronous method is implementable in a multiprocessor system, allowing for communication and computation delays among the processors. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Tai, Xue Cheng Tseng, Paul |
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Article |
author |
Tai, Xue Cheng Tseng, Paul |
author_sort |
Tai, Xue Cheng |
title |
Convergence rate analysis of an asynchronous space decomposition method for convex minimization |
title_short |
Convergence rate analysis of an asynchronous space decomposition method for convex minimization |
title_full |
Convergence rate analysis of an asynchronous space decomposition method for convex minimization |
title_fullStr |
Convergence rate analysis of an asynchronous space decomposition method for convex minimization |
title_full_unstemmed |
Convergence rate analysis of an asynchronous space decomposition method for convex minimization |
title_sort |
convergence rate analysis of an asynchronous space decomposition method for convex minimization |
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2009 |
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https://hdl.handle.net/10356/90754 http://hdl.handle.net/10220/6054 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2002&volume=71&issue=239&spage=1105&epage=1135&aulast=Tai&aufirst=%20X%20%2DC&auinit=&title=Mathematics%20of%20Computation&atitle=Convergence%20rate%20analysis%20of%20an%20asynchronous%20space%20decomposition%20method%20for%20convex%20minimization&sici. |
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