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Convergence rate analysis of an asynchronous space decomposition method for convex minimization

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Convergence rate analysis of an asynchronous space decomposition method for convex minimization

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Title: Convergence rate analysis of an asynchronous space decomposition method for convex minimization
Author: Tai, Xue Cheng; Tseng, Paul
Copyright year: 2001
Abstract: 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.
Subject: DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis.
Type: Journal Article
Series/ Journal Title: Mathematics of computation.
School: School of Physical and Mathematical Sciences
Rights: Mathematics of Computation © copyright 2001 American Mathematical Society. The journal's website is located at http://www.ams.org/mcom/.
Version: Published version

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