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Restarting the accelerated coordinate descent method with a rough strong convexity estimate

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  • Olivier Fercoq

    (Université Paris-Saclay)

  • Zheng Qu

    (The University of Hong Kong)

Abstract

We propose new restarting strategies for the accelerated coordinate descent method. Our main contribution is to show that for a well chosen sequence of restarting times, the restarted method has a nearly geometric rate of convergence. A major feature of the method is that it can take profit of the local quadratic error bound of the objective function without knowing the actual value of the error bound. We also show that under the more restrictive assumption that the objective function is strongly convex, any fixed restart period leads to a geometric rate of convergence. Finally, we illustrate the properties of the algorithm on a regularized logistic regression problem and on a Lasso problem.

Suggested Citation

  • Olivier Fercoq & Zheng Qu, 2020. "Restarting the accelerated coordinate descent method with a rough strong convexity estimate," Computational Optimization and Applications, Springer, vol. 75(1), pages 63-91, January.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00137-2
    DOI: 10.1007/s10589-019-00137-2
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Ion Necoara & Yurii Nesterov & François Glineur, 2019. "Linear convergence of first order methods for non-strongly convex optimization," LIDAM Reprints CORE 3000, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Pavel Dvurechensky & Alexander Gasnikov, 2016. "Stochastic Intermediate Gradient Method for Convex Problems with Stochastic Inexact Oracle," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 121-145, October.
    5. Qihang Lin & Lin Xiao, 2015. "An adaptive accelerated proximal gradient method and its homotopy continuation for sparse optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 633-674, April.
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    Cited by:

    1. A. Scagliotti & P. Colli Franzone, 2022. "A piecewise conservative method for unconstrained convex optimization," Computational Optimization and Applications, Springer, vol. 81(1), pages 251-288, January.

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