In this paper, we present a convergence rate analysis for the inexact Krasnosel'skiĭ–Mann
iteration built from non-expansive operators. The presented results include two main parts …

Recently, several authors have shown local and global convergence rate results for Douglas–
Rachford splitting under strong monotonicity, Lipschitz continuity, and cocoercivity …

This manuscript is concerned with convergence analysis of first-order operator splitting
methods that are ubiquitous in modern non-smooth optimization. It consists of three main …

Over the past decades, operator splitting methods have become ubiquitous for non-smooth
optimization owing to their simplicity and efficiency. In this paper, we consider the Forward …

Convex optimization has become ubiquitous in most quantitative disciplines of science,
including variational image processing. Proximal splitting algorithms are becoming popular …

Abstract The Douglas–Rachford splitting algorithm was originally proposed in 1956 to solve
a system of linear equations arising from the discretization of a partial differential equation …

The problem of finding a minimizer of the sum of two convex functions–or, more generally,
that of finding a zero of the sum of two maximally monotone operators–is of central …

Monotone inclusion problems occur in many areas of optimization and variational analysis.
Splitting methods, which utilize resolvents or proximal mappings of the underlying operators …

This paper presents a new method for efficiently computing the response of a perturbed
dynamic system. The method is based on predicting the convergence of a Neumann series …

A method is presented to improve the estimates of material properties, dimensions, and
other model parameters for linear vibrating systems. The method improves the estimates of a …