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Convergence rate of a relaxed inertial proximal algorithm for convex minimization

Author

Listed:
  • Hedy Attouch

    (IMAG - Institut Montpelliérain Alexander Grothendieck - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique)

  • Alexandre Cabot

    (IMB - Institut de Mathématiques de Bourgogne [Dijon] - UB - Université de Bourgogne - UBFC - Université Bourgogne Franche-Comté [COMUE] - CNRS - Centre National de la Recherche Scientifique)

Abstract

In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.

Suggested Citation

  • Hedy Attouch & Alexandre Cabot, 2020. "Convergence rate of a relaxed inertial proximal algorithm for convex minimization," Post-Print hal-02415789, HAL.
    • Handle: RePEc:hal:journl:hal-02415789
    DOI: 10.1080/02331934.2019.1696337
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    Citations

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    Cited by:

    1. Fan Wu & Wei Bian, 2023. "Smoothing Accelerated Proximal Gradient Method with Fast Convergence Rate for Nonsmooth Convex Optimization Beyond Differentiability," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 539-572, May.
    2. M. Marques Alves & Jonathan Eckstein & Marina Geremia & Jefferson G. Melo, 2020. "Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms," Computational Optimization and Applications, Springer, vol. 75(2), pages 389-422, March.
    3. S.-M. Grad & F. Lara & R. T. Marcavillaca, 2023. "Relaxed-inertial proximal point type algorithms for quasiconvex minimization," Journal of Global Optimization, Springer, vol. 85(3), pages 615-635, March.

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