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

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  • Francisco J. Aragón Artacho

    (University of Alicante)

  • Rubén Campoy

    (University of Alicante)

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.

Suggested Citation

  • Francisco J. Aragón Artacho & Rubén Campoy, 2019. "Computing the Resolvent of the Sum of Maximally Monotone Operators with the Averaged Alternating Modified Reflections Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 709-726, June.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01481-3
    DOI: 10.1007/s10957-019-01481-3
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    References listed on IDEAS

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    1. Francisco J. Aragón Artacho & Rubén Campoy, 2018. "A new projection method for finding the closest point in the intersection of convex sets," Computational Optimization and Applications, Springer, vol. 69(1), pages 99-132, January.
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    Cited by:

    1. Francisco J. Aragón Artacho & Rubén Campoy & Matthew K. Tam, 2021. "Strengthened splitting methods for computing resolvents," Computational Optimization and Applications, Springer, vol. 80(2), pages 549-585, November.
    2. Rubén Campoy, 2022. "A product space reformulation with reduced dimension for splitting algorithms," Computational Optimization and Applications, Springer, vol. 83(1), pages 319-348, September.
    3. Rieger, Janosch & Tam, Matthew K., 2020. "Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions," Applied Mathematics and Computation, Elsevier, vol. 381(C).

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