On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

Boţ, Radu Ioan; Csetnek, Ernö Robert; Heinrich, André

doi:10.48550/arxiv.1303.2875

Cited by 2 publications

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“…we can interpret the CP-algorithm as a fixed point iteration with an over-relaxation step in line (7).…”

Section: Preliminariesmentioning

confidence: 99%

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A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems

Hohage,

Homann

2014

Preprint

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For a Hilbert space setting Chambolle and Pock introduced an attractive first-order algorithm which solves a convex optimization problem and its Fenchel dual simultaneously. We present a generalization of this algorithm to Banach spaces. Moreover, under certain conditions we prove strong convergence as well as convergence rates. Due to the generalization the method becomes efficiently applicable for a wider class of problems. This fact makes it particularly interesting for solving ill-posed inverse problems on Banach spaces by Tikhonov regularization or the iteratively regularized Newton-type method, respectively.

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“…we can interpret the CP-algorithm as a fixed point iteration with an over-relaxation step in line (7).…”

Section: Preliminariesmentioning

confidence: 99%

“…There exists generalizations of this algorithm in order to solve monotone inclusion problems ( [7,30]) and to the case of nonlinear operators T ( [31]). Recently, Lorenz and Pock ([19]) proposed a quite general forward-backward algorithm for monotone inclusion problems with CP as an special case.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems

Hohage,

Homann

2014

Preprint

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“…In particular, several primal-dual splitting schemes were designed such as those in [6,7] or [8] in the context of convex optimization. See also [9,10] for convergence rates analysis. The authors in [11,12] analyze the iteration-complexity of the hybrid proximal extragradient (HPE) method proposed by Solodov and Svaiter.…”

Section: Introduction 1problem Statementmentioning

confidence: 99%

Iteration-Complexity of a Generalized Forward Backward Splitting Algorithm

Liang,

Fadili,

Peyré

2013

Preprint

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In this paper, we analyze the iteration-complexity of Generalized Forward-Backward (GFB) splitting algorithm, as proposed in [2], for minimizing a large class of composite objectives f `řn i"1 h i on a Hilbert space, where f has a Lipschitzcontinuous gradient and the h i 's are simple (i.e. their proximity operators are easy to compute). We derive iterationcomplexity bounds (pointwise and ergodic) for the inexact version of GFB to obtain an approximate solution based on an easily verifiable termination criterion. Along the way, we prove complexity bounds for relaxed and inexact fixed point iterations built from composition of nonexpansive averaged operators. These results apply more generally to GFB when used to find a zero of a sum of n ą 0 maximal monotone operators and a co-coercive operator on a Hilbert space. The theoretical findings are exemplified with experiments on video processing.

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On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

Cited by 2 publications

References 0 publications

A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems

A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems

Iteration-Complexity of a Generalized Forward Backward Splitting Algorithm

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