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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Main Authors: Tai, Xue Cheng, Tseng, Paul
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2009
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Online Access:https://hdl.handle.net/10356/90754
http://hdl.handle.net/10220/6054
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spelling 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
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
spellingShingle DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
Tai, Xue Cheng
Tseng, Paul
Convergence rate analysis of an asynchronous space decomposition method for convex minimization
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Tai, Xue Cheng
Tseng, Paul
format 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
publishDate 2009
url 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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