Inertial-relaxed splitting for composite monotone inclusions

In a similar spirit of the extension of the proximal point method developed by Alves et al. \cite{alvegm20}, we propose in this work an Inertial-Relaxed primal-dual splitting method to address the problem of decomposing the minimization of the sum of three convex functions, one of them being smooth, and considering a general coupling subspace. A … Read more

A survey on operator splitting and decomposition of convex programs

Many structured convex minimization problems can be modeled by the search of a zero of the sum of two monotone operators. Operator splitting methods have been designed to decompose and regularize at the same time these kind of models. We review here these models and the classical splitting methods. We focus on the numerical sensitivity … Read more

Global and adaptive scaling in a separable augmented lagrangian algorithm

In this paper, we analyze the numerical behaviour of a separable Augmented Lagrangian algorithm with multiple scaling parameters, different parameters associated with each dualized coupling constraint as well as with each subproblem. We show that an optimal superlinear rate of convergence can be theoretically attained in the twice differentiable case and propose an adaptive scaling … Read more