This paper gives a unified convergence analysis of additive Schwarz methods for general
convex optimization problems. Resembling the fact that additive Schwarz methods for linear …

Group convolution has been widely used in order to reduce the computation time of
convolution, which takes most of the training time of convolutional neural networks …

This paper presents a novel backtracking strategy for additive Schwarz methods for general
convex optimization problems as an acceleration scheme. The proposed backtracking …

Total variation minimization is standard in mathematical imaging and there have been
numerous researches over the last decades. In order to process large-scale images in real …

Based on an observation that additive Schwarz methods for general convex optimization
can be interpreted as gradient methods, we propose an acceleration scheme for additive …

This paper presents the domain decomposition methods (DDMs) for achieving fast parallel
computing on multi-core computers when dealing with the multi-phase labeling problem. To …

We concern with fast domain decomposition methods for solving the total variation
minimization problems in image processing. By decomposing the image domain into non …

We present new convergence analyses for subspace correction methods for semicoercive
and nearly semicoercive convex optimization problems, generalizing the theory of singular …

We consider sequential and parallel decomposition methods for a dual problem of a general
total variation minimization problem with applications in several image processing tasks, like …

Abstract Domain decomposition is one of the most efficient techniques to derive efficient
methods for large-scale problems. In this chapter such decomposition methods for the …