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Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization

Author

Listed:
  • Cheik Traoré

    (Università degli Studi di Genova)

  • Saverio Salzo

    (DIAG, Sapienza Università di Roma)

  • Silvia Villa

    (Università degli Studi di Genova)

Abstract

In this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex objective function, where the block-coordinates are updated asynchronously and randomly according to an arbitrary probability distribution. We prove that the iterates generated by the algorithm form a stochastic quasi-Fejér sequence and thus converge almost surely to a minimizer of the objective function. Moreover, we prove a general sublinear rate of convergence in expectation for the function values and a linear rate of convergence in expectation under an error bound condition of Tseng type. Under the same condition strong convergence of the iterates is provided as well as their linear convergence rate.

Suggested Citation

  • Cheik Traoré & Saverio Salzo & Silvia Villa, 2023. "Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization," Computational Optimization and Applications, Springer, vol. 86(1), pages 303-344, September.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:1:d:10.1007_s10589-023-00489-w
    DOI: 10.1007/s10589-023-00489-w
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    References listed on IDEAS

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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
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