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Efficiency of coordinate descent methods on huge-scale optimization problems

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  • NESTEROV, Yurii

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

Abstract

In this paper we propose new methods for solving huge-scale optimization problems. For problems of this size, even the simplest full-dimensional vector operations are very expensive. Hence, we propose to apply an optimization technique based on random partial update of decision variables. For these methods, we prove the global estimates for the rate of convergence. Surprisingly enough, for certain classes of objective functions, our results are better than the standard worst-case bounds for deterministic algorithms. We present constrained and unconstrained versions of the method, and its accelerated variant. Our numerical test confirms a high efficiency of this technique on problems of very big size.

Suggested Citation

  • NESTEROV, Yurii, 2010. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Discussion Papers CORE 2010002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2010002
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2010.html
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    Cited by:

    1. D. Leventhal & A. S. Lewis, 2010. "Randomized Methods for Linear Constraints: Convergence Rates and Conditioning," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 641-654, August.
    2. Amir Beck, 2014. "The 2-Coordinate Descent Method for Solving Double-Sided Simplex Constrained Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 892-919, September.

    More about this item

    Keywords

    Convex optimization; coordinate relaxation; worst-case efficiency estimates; fast gradient schemes; Google problem;
    All these keywords.

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