Journal of Convex Analysis 27 (2020), No. 3, 893--922
Copyright Heldermann Verlag 2020
A Unified Splitting Algorithm for Composite Monotone Inclusions
Ernesto Oré-Albornoz
IMCA, Universidad Nacional de Ingeniería, Lima, Peru
and: LIMOS, Université Clermont Auvergne, Clermont-Ferrand, France
Philippe Mahey
LIMOS, Université Clermont Auvergne, Clermont-Ferrand, France
mahey@isima.fr
Eladio Ocana-Anaya
IMCA, Universidad Nacional de Ingeniería, Lima, Peru
Operator splitting methods have been recently concerned with inclusions problems based on composite operators made of the sum of two monotone operators, one of them associated with a linear transformation. We analyze here a general and new splitting method which indeed splits both operator proximal steps, and avoiding costly numerical algebra on the linear operator. The family of algorithms induced by our generalized setting includes known methods like Chambolle-Pock primal-dual algorithm and Shefi-Teboulle Proximal Alternate Direction Method of Multipliers. The study of the ergodic and non ergodic convergence rates show similar rates with the classical Douglas-Rachford splitting scheme. We end with an application to a multi-block convex optimization model which leads to a generalized Separable Augmented Lagrangian Algorithm.
Keywords: Splitting methods, monotone inclusions, convergence analysis.
MSC: 90C25, 90C30, 65K13.
[ Fulltext-pdf (196 KB)] for subscribers only.