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Computing the resolvent of composite operators

Author

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  • Abdellatif Moudafi

    (Ceregmia-Departement scientifque, Universite des Antilles et de la Guyane, 97275 Schoelcher, Martinique)

Abstract

Based in a very recent paper by Micchelli et al. [7], we present an algorithmic approach for computing the resolvent of composite operators: the composition of a monotone operator and a continuous linear mapping. The proposed algorithm can be used, for example, for solving problems arising in image processing and trac equilibrium. Furthermore, our algorithm gives an alternative to Dykstra-like method for evaluating the resolvent of the sum of two maximal monotone operators.

Suggested Citation

  • Abdellatif Moudafi, 2014. "Computing the resolvent of composite operators," Documents de Travail 2014-02, CEREGMIA, Université des Antilles et de la Guyane.
    • Handle: RePEc:crg:wpaper:dt2014-02
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    File URL: http://www2.univ-ag.fr/RePEc/DT/DT2014-02_Moudafi.pdf
    File Function: First version, 2014
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    References listed on IDEAS

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    1. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
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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. Yixuan Yang & Yuchao Tang & Chuanxi Zhu, 2019. "Iterative Methods for Computing the Resolvent of Composed Operators in Hilbert Spaces," Mathematics, MDPI, vol. 7(2), pages 1-16, February.

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