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On an Extension of a Spare Regularization Model

Author

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  • Abdellatif Moudafi

    (CNRS-L.I.S UMR 7296, Aix Marseille Université, Campus Universitaire de Saint-Jérôme, 13397 Marseille, France)

Abstract

In this paper, we would first like to promote an interesting idea for identifying the local minimizer of a non-convex optimization problem with the global minimizer of a convex optimization one. Secondly, to give an extension of their sparse regularization model for inverting incomplete Fourier transforms introduced. Thirdly, following the same lines, to develop convergence guaranteed efficient iteration algorithm for solving the resulting nonsmooth and nonconvex optimization problem but here using applied nonlinear analysis tools. These both lead to a simplification of the proofs and to make a connection with classical works in this filed through a startling comment.

Suggested Citation

  • Abdellatif Moudafi, 2023. "On an Extension of a Spare Regularization Model," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4285-:d:1259682
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    References listed on IDEAS

    as
    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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    1. 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.

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