douglas-rachford splitting – Page 2

Convergence rate analysis of several splitting schemes

Published: 2014/06/18, Updated: 2014/08/20

Convex and Nonsmooth Optimization alternating direction method of multipliers, averaged operator, douglas-rachford splitting, fixed point algorithm, krasnosel'skii-mann algorithm, little-o convergence, nonexpansive operator, peaceman-rachford splitting

Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable algorithms, which often obtain nearly state-of-the-art performance. … Read more

A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators

Published: 2012/12/03

Radu Ioan Bot

Christopher Hendrich

Convex Optimization convex optimization, douglas-rachford splitting, fenchel duality, monotone inclusion

In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however applied in different underlying Hilbert spaces. Most importantly, the algorithms allow to process the bounded linear operators and the set-valued operators occurring in the … Read more