Solving monotone inclusions involving parallel sums of linearly composed maximally monotone operators

Radu Ioan  Boţ; Christopher  Hendrich

doi:10.3934/ipi.2016014

Article Contents

2016, Volume 10, Issue 3: 617-640. Doi: 10.3934/ipi.2016014

This issue Previous Article On the stability of some imaging functionals Next Article The inverse problem for electroseismic conversion: Stable recovery of the conductivity and the electrokinetic mobility parameter

Solving monotone inclusions involving parallel sums of linearly composed maximally monotone operators

Radu Ioan Boţ^1, and
Christopher Hendrich^2,

1.
University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, A-1090 Vienna
2.
Chemnitz University of Technology, Department of Mathematics, D-09107 Chemnitz

Received: May 31, 2014

Revised: March 31, 2016

Published: July 2016

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Abstract

The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some elaborated splitting techniques, all of the operators occurring in the problem formulation are processed individually via forward or backward steps. The treatment of parallel sums of linearly composed maximally monotone operators is motivated by applications in imaging which involve first- and second-order total variation functionals, to which a special attention is given.

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Mathematics Subject Classification: Primary: 90C25, 90C46; Secondary: 47A52.

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