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Global and uniform convergence of subspace correction methods for some convex optimization problems


Authors: Xue-Cheng Tai and Jinchao Xu
Journal: Math. Comp. 71 (2002), 105-124
MSC (2000): Primary 65N22, 65N55, 65K10, 65J15
DOI: https://doi.org/10.1090/S0025-5718-01-01311-4
Published electronically: May 11, 2001
MathSciNet review: 1862990
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Abstract:

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.


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Additional Information

Xue-Cheng Tai
Affiliation: Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5007, Bergen, Norway
Email: tai@mi.uib.no

Jinchao Xu
Affiliation: Center for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email: xu@math.psu.edu

DOI: https://doi.org/10.1090/S0025-5718-01-01311-4
Keywords: Parallel, multigrid, domain decomposition, nonlinear, elliptic equation, space decomposition, convex optimization
Received by editor(s): March 10, 1998
Received by editor(s) in revised form: September 15, 1999, and March 24, 2000
Published electronically: May 11, 2001
Additional Notes: The work of the first author was partially supported by the Norwegian Research Council Strategic Institute Program within Inverse Problems at RF–Rogaland Research.
The work of the second author was partially supported by NSF DMS-9706949 NSF ACI-9800244, NASA NAG2-1236 through Pennsylvania State University.
Article copyright: © Copyright 2001 American Mathematical Society

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