HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

A Parallel Inertial Proximal Optimization Method

Abstract : The Douglas-Rachford algorithm is a popular iterative method for finding a zero of a sum of two maximal monotone operators defined on a Hilbert space. In this paper, we propose an extension of this algorithm including inertia parameters and develop parallel versions to deal with the case of a sum of an arbitrary number of maximal operators. Based on this algorithm, parallel proximal algorithms are proposed to minimize over a linear subspace of a Hilbert space the sum of a finite number of proper, lower semicontinuous convex functions composed with linear operators. It is shown that particular cases of these methods are the simultaneous direction method of multipliers proposed by Stetzer et al., the parallel proximal algorithm developed by Combettes and Pesquet, and a parallelized version of an algorithm proposed by Attouch and Soueycatt.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-00790702
Contributor : Nelly Pustelnik Connect in order to contact the contributor
Submitted on : Thursday, February 21, 2013 - 8:59:19 AM
Last modification on : Saturday, January 15, 2022 - 3:58:09 AM
Long-term archiving on: : Sunday, April 2, 2017 - 3:08:15 AM

File

parallelin_v3.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00790702, version 1

Citation

Jean-Christophe Pesquet, Nelly Pustelnik. A Parallel Inertial Proximal Optimization Method. Pacific journal of optimization, Yokohama Publishers, 2012, 8 (2), pp.273-305. ⟨hal-00790702⟩

Share

Metrics

Record views

450

Files downloads

515