http://dx.doi.org/10.1137/100814494">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective

Language

English

Abstract

Recently, some primal-dual algorithms have been proposed for solving a saddle-point problem, with particular applications in the area of total variation image restoration. This paper focuses on the convergence analysis of these primal-dual algorithms and shows that their involved parameters (including step sizes) can be significantly enlarged if some simple correction steps are supplemented. Some new primal-dual-based methods are thus proposed for solving the saddle-point problem. We show that these new methods are of the contraction type: the iterative sequences generated by these new methods are contractive with respect to the solution set of the saddle-point problem. The global convergence of these new methods thus can be obtained within the analytic framework of contraction-type methods. The novel study on these primal-dual algorithms from the perspective of contraction methods substantially simplifies existing convergence analysis. Finally, we show the efficiency of the new methods numerically. © 2012 Society for Industrial and Applied Mathematics.

Keywords

Contraction method, Image restoration, Primal-dual method, Proximal point algorithm, Saddle point problem, Total variation

Publication Date

2012

Source Publication Title

SIAM Journal on Imaging Sciences

Volume

5

Issue

1

Start Page

119

End Page

149

Publisher

Society for Industrial and Applied Mathematics

ISSN (electronic)

19364954

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