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ADMM for monotone operators: convergence analysis and rates

Radu Ioan Bot(radu.bot***at***univie.ac.at)
Ernö Robert Csetnek(ernoe.robert.csetnek***at***univie.ac.at)

Abstract: We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We show that a number of primal-dual algorithms for monotone inclusions and also the classical ADMM numerical scheme for convex optimization problems, along with some of its variants, can be embedded in this unifying scheme. While in the first part of the paper convergence results for the iterates are reported, the second part is devoted to the derivation of convergence rates obtained by combining variable metric techniques with strategies based on suitable choice of dynamical step sizes.

Keywords: monotone operators, primal-dual algorithm, ADMM algorithm, subdifferential, convex optimization, Fenchel duality

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

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Entry Submitted: 05/04/2017
Entry Accepted: 05/04/2017
Entry Last Modified: 05/04/2017

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