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A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions

Antonin Chambolle (antonin.chambolle***at***cmap.polytechnique.fr)
Thomas Pock (pock***at***icg.tugraz.at)

Abstract: We analyze alternating descent algorithms for minimizing the sum of a quadratic function and block separable non-smooth functions. In case the quadratic interactions between the blocks are pairwise, we show that the schemes can be accelerated, leading to improved convergence rates with respect to related accelerated parallel proximal descent. As an application we obtain very fast algorithms for computing the proximity operator of the 2D and 3D total variation.

Keywords: Block coordinate descent, accelerated gradient methods, total variation

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 01/03/2015
Entry Accepted: 01/03/2015
Entry Last Modified: 01/06/2015

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