Global and uniform convergence of subspace correction methods for some convex optimization problems
Mathematics of Computation
A domain decomposition method for a kind of optimization problems
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
On monotone iteration and Schwarz methods for nonlinear parabolic PDEs
Journal of Computational and Applied Mathematics
Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation
Journal of Mathematical Imaging and Vision
A Nonlinear Multigrid Method for Total Variation Minimization from Image Restoration
Journal of Scientific Computing
Schwarz methods for inequalities with contraction operators
Journal of Computational and Applied Mathematics
A Parallel Implementation of the PBSGDS Method for Solving CBAU Optimization Problems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Domain decomposition methods with graph cuts algorithms for total variation minimization
Advances in Computational Mathematics
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
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Convergence of a space decomposition method is proved for a class of convex programming problems. A space decomposition refers to a method that decomposes a space into a sum of subspaces, which could be a domain decomposition or a multilevel method when applied to partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems, and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems.