A Population-Based Stochastic Coordinate Descent Method

  • Ana Maria A. C. RochaEmail author
  • M. Fernanda P. Costa
  • Edite M. G. P. Fernandes
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


This paper addresses the problem of solving a bound constrained global optimization problem by a population-based stochastic coordinate descent method. To improve efficiency, a small subpopulation of points is randomly selected from the original population, at each iteration. The coordinate descent directions are based on the gradient computed at a special point of the subpopulation. This point could be the best point, the center point or the point with highest score. Preliminary numerical experiments are carried out to compare the performance of the tested variants. Based on the results obtained with the selected problems, we may conclude that the variants based on the point with highest score are more robust and the variants based on the best point less robust, although they win on efficiency but only for the simpler and easy to solve problems.


Global optimization Stochastic coordinate descent 



This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the Projects Scope: UID/CEC/00319/2019 and UID/MAT/00013/2013.


  1. 1.
    Bottou, L., Curtis, F.E., Nocedal, J.: Optimization methods for large-scale machine learning. Technical Report arXiv:1606.04838v3, Computer Sciences Department, University of Wisconsin-Madison (2018)
  2. 2.
    Rocha, A.M.A.C., Costa, M.F.P., Fernandes, E.M.G.P.: A stochastic coordinate descent for bound constrained global optimization. AIP Conf. Proc. 2070, 020014 (2019)Google Scholar
  3. 3.
    Kvasov, D.E., Mukhametzhanov, M.S.: Metaheuristic vs. deterministic global optimization algorithms: the univariate case. Appl. Math. Comput. 318, 245–259 (2018)Google Scholar
  4. 4.
    Nesterov, Y.: Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J. Optim. 22(2), 341–362 (2012)Google Scholar
  5. 5.
    Wright, S.J.: Coordinate descent algorithms. Math. Program. Series B 151(1), 3–34 (2015)Google Scholar
  6. 6.
    Liu, H., Xu, S., Chen, X., Wang, X., Ma, Q.: Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy. Struct. Multidisc. Optim. 55(1), 155–177 (2017)Google Scholar
  7. 7.
    Ali, M.M., Khompatraporn, C., Zabinsky, Z.B.: A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J. Glob. Optim. 31(4), 635–672 (2005)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Ana Maria A. C. Rocha
    • 1
    • 2
    Email author
  • M. Fernanda P. Costa
    • 3
    • 4
  • Edite M. G. P. Fernandes
    • 1
  1. 1.ALGORITMI CenterUniversity of MinhoBragaPortugal
  2. 2.Department of Production and SystemsUniversity of MinhoBragaPortugal
  3. 3.Centre of MathematicsUniversity of MinhoBragaPortugal
  4. 4.Department of MathematicsGuimarãesPortugal

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