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Efficiency of Accelerated Coordinate Descent Method on Structured Optimization Problems

Author

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  • NESTEROV, Yurii

    (Université catholique de Louvain, CORE, Belgium)

  • STICH, Sebastian

    (Université catholique de Louvain, CORE, Belgium)

Abstract

In this paper we prove a new complexity bound for a variant of Accelerated Coordinate Descent Method [7]. We show that this method often outperforms the standard Fast Gradient Methods (FGM, [3, 6]) on optimization problems with dense data. In many important situations, the computational expenses of oracle and method itself at each iteration of our scheme are perfectly balanced (both depend linearly on dimensions of the problem). As application examples, we consider unconstrained convex quadratic minimization, and the problems arising in Smoothing Technique [6]. On some special problem instances, the provable acceleration factor with respect to FGM can reach the square root of the number of variables. Our theoretical conclusions are confirmed by numerical experiments.

Suggested Citation

  • NESTEROV, Yurii & STICH, Sebastian, 2016. "Efficiency of Accelerated Coordinate Descent Method on Structured Optimization Problems," LIDAM Discussion Papers CORE 2016003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2016003
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2016.html
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