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A New Approach for Proximal Split Minimization Problems

Author

Listed:
  • Abdellatif Moudafi

    (Laboratoire d’Informatique et Systèmes (LIS UMR 7020 CNRS/AMU/UTLN), Aix-Marseille Université, 13288 Marseille, France)

  • André Weng-Law

    (Laboratoire MEMIAD, Université des Antilles, Campus de Schoelcher, 97233 Schoelcher, Cedex, France)

Abstract

We provide an alternative formulation of proximal split minimization problems, a very recently developed and appealing strategy that relies on an infimal post-composition approach. Then, forward–backward and Douglas–Rachford splitting algorithms will guide both the design and analysis of some split numerical methods. We provide evidence of globally weak convergence and the fact that these algorithms can be equipped with relaxed and/or inertial steps, leading to improved convergence guarantees.

Suggested Citation

  • Abdellatif Moudafi & André Weng-Law, 2025. "A New Approach for Proximal Split Minimization Problems," Mathematics, MDPI, vol. 13(1), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:144-:d:1559029
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    References listed on IDEAS

    as
    1. A. Moudafi & M. Théra, 1997. "Finding a Zero of The Sum of Two Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 425-448, August.
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