Diagonal preconditioning for first order primal-dual algorithms in convex optimization

Authors:
Thomas Pock;Antonin Chambolle
Affiliations:
Institute for Computer Graphics and Vision, Graz University of Technology, Austria;CMAP & CNRS, ÉÉcole Polytechnique, France
Venue:
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Year:
2011

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Abstract

In this paper we study preconditioning techniques for the first-order primal-dual algorithm proposed in [5]. In particular, we propose simple and easy to compute diagonal preconditioners for which convergence of the algorithm is guaranteed without the need to compute any step size parameters. As a by-product, we show that for a certain instance of the preconditioning, the proposed algorithm is equivalent to the old and widely unknown alternating step method for monotropic programming [7]. We show numerical results on general linear programming problems and a few standard computer vision problems. In all examples, the preconditioned algorithm significantly outperforms the algorithm of [5].