We investigate additive Schwarz methods for semilinear elliptic problems with convex
energy functionals, which have wide scientific applications. A key observation is that the …

We consider additive Schwarz methods for boundary value problems involving the-
Laplacian. While existing theoretical estimates suggest a sublinear convergence rate for …

Fourth-order variational inequalities are encountered in various scientific and engineering
disciplines, including elliptic optimal control problems and plate obstacle problems. In this …

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

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 …

Projected gradient descent and its Riemannian variant belong to a typical class of methods
for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated …

In this paper, we study a speed restart scheme for an inertial system with Hessian-driven
damping. We establish a linear convergence rate for the function values along the restarted …

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

We consider additive Schwarz methods for boundary value problems involving the $ p $-
Laplacian. Although the existing theoretical estimates indicate a sublinear convergence rate …

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 …