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Towards split monotone inclusions with composite operators: a regularization approach

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  • Abdellatif Moudafi

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

Abstract

Relying on the Yosida approximate, we present an algorithmic approach for nding solutions of split monotone problems involving the composite of a monotone operator and a bounded linear mapping. The proposed algorithms can be used for solving problems arising in image processing and in location theory. Convergence results are provided and some remarks on potential developments based on the variational composition, whose utility was demonstrated in [1] by applications to the theory of measurable multifunctions and elliptic PDEs with singular coecients, are stated.

Suggested Citation

  • Abdellatif Moudafi, 2014. "Towards split monotone inclusions with composite operators: a regularization approach," Documents de Travail 2014-01, CEREGMIA, Université des Antilles et de la Guyane.
    • Handle: RePEc:crg:wpaper:dt2014-01
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    File URL: http://www2.univ-ag.fr/RePEc/DT/DT2014-01_Moudafi.pdf
    File Function: First version, 2014
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    References listed on IDEAS

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    1. Isao Yamada & Masahiro Yukawa & Masao Yamagishi, 2011. "Minimizing the Moreau Envelope of Nonsmooth Convex Functions over the Fixed Point Set of Certain Quasi-Nonexpansive Mappings," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 345-390, Springer.
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