Optimal rates of linear convergence of the averaged alternating modified reflections method for two subspaces

Artacho, Francisco J. Aragón; Campoy, Rubén

doi:10.1007/s11075-018-0608-x

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2019

2025

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Cited by 6 publications

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“…The rate of convergence of the AAMR algorithm for the case of two subspaces has been recently analyzed in [2]. If the algorithm is run with an optimal selection of its parameters, its rate of convergence was shown to be better than the one of other projection methods.…”

Section: Introductionmentioning

confidence: 99%

Computing the Resolvent of the Sum of Maximally Monotone Operators with the Averaged Alternating Modified Reflections Algorithm

Artacho

Campoy

2019

J Optim Theory Appl

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The averaged alternating modified reflections algorithm is a projection method for finding the closest point in the intersection of closed and convex sets to a given point in a Hilbert space. In this work, we generalize the scheme so that it can be used to compute the resolvent of the sum of two maximally monotone operators. This gives rise to a new splitting method, which is proved to be strongly convergent. A standard product space reformulation permits to apply the method for computing the resolvent of a finite sum of maximally monotone operators. Based on this, we propose two variants of such parallel splitting method.

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Section: Introductionmentioning

confidence: 99%