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Performance of first- and second-order methods for $$\ell _1$$ ℓ 1 -regularized least squares problems

Author

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  • Kimon Fountoulakis

    (The University of Edinburgh)

  • Jacek Gondzio

    (The University of Edinburgh
    NASK Research Institute)

Abstract

We study the performance of first- and second-order optimization methods for $$\ell _1$$ ℓ 1 -regularized sparse least-squares problems as the conditioning of the problem changes and the dimensions of the problem increase up to one trillion. A rigorously defined generator is presented which allows control of the dimensions, the conditioning and the sparsity of the problem. The generator has very low memory requirements and scales well with the dimensions of the problem.

Suggested Citation

  • Kimon Fountoulakis & Jacek Gondzio, 2016. "Performance of first- and second-order methods for $$\ell _1$$ ℓ 1 -regularized least squares problems," Computational Optimization and Applications, Springer, vol. 65(3), pages 605-635, December.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:3:d:10.1007_s10589-016-9853-x
    DOI: 10.1007/s10589-016-9853-x
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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. Jacek Gondzio, 2012. "Matrix-free interior point method," Computational Optimization and Applications, Springer, vol. 51(2), pages 457-480, March.
    4. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Carrizosa, Emilio & Guerrero, Vanesa & Romero Morales, Dolores, 2019. "Visualization of complex dynamic datasets by means of mathematical optimization," Omega, Elsevier, vol. 86(C), pages 125-136.
    2. Kimon Fountoulakis & Rachael Tappenden, 2018. "A flexible coordinate descent method," Computational Optimization and Applications, Springer, vol. 70(2), pages 351-394, June.

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