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A Class of Randomized Primal-Dual Algorithms for Distributed Optimization

Jean-Christophe Pesquet (jean-christophe.pesquet***at***univ-paris-est.fr)
Audrey Repetti (audrey.repetti***at***univ-paris-est.fr)

Abstract: Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide array of monotone inclusion problems. These methods rely on a sweep of blocks of variables which are activated at each iteration according to a random rule, and they allow stochastic errors in the evaluation of the involved operators. Then, this framework is employed to derive block-coordinate primal-dual proximal algorithms for solving composite convex variational problems. The resulting algorithm implementations may be useful for reducing computational complexity and memory requirements. Furthermore, we show that the proposed approach can be used to develop novel asynchronous distributed primal-dual algorithms in a multi-agent context.

Keywords: Block-coordinate algorithm, convex optimization, distributed algorithm, monotone operator, preconditioning, primal-dual algorithm, stochastic quasi-Fejér sequence

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Stochastic Programming


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Entry Submitted: 06/24/2014
Entry Accepted: 06/24/2014
Entry Last Modified: 10/25/2014

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