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

Francisco J. Aragón Artacho () and Rubén Campoy ()
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Francisco J. Aragón Artacho: University of Alicante
Rubén Campoy: University of Alicante

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 3, No 1, 709-726

Abstract: Abstract 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.

Keywords: Maximally monotone operator; Resolvent; Averaged alternating modified reflections algorithm; Douglas–Rachford algorithm; Splitting method; 47H05; 47J25; 65K05; 47N10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-019-01481-3

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