IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v69y2017i1d10.1007_s10898-016-0465-x.html
   My bibliography  Save this article

Parallel distributed block coordinate descent methods based on pairwise comparison oracle

Author

Listed:
  • Kota Matsui

    (Nagoya University)

  • Wataru Kumagai

    (Kanagawa University)

  • Takafumi Kanamori

    (Nagoya University)

Abstract

This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. Our algorithm uses only pairwise comparison of function values, which tells us only the order of function values over two points, and does not require computation of a function value itself or a gradient. Our algorithm iterates two steps: the direction estimate step and the search step. In the direction estimate step, a Newton-type search direction is estimated through a block coordinate descent-based computation method with the pairwise comparison. In the search step, a numerical solution is updated along the estimated direction. The computation in the direction estimate step can be easily parallelized, and thus, the algorithm works efficiently to find the minimizer of the objective function. Also, we theoretically derive an upper bound of the convergence rate for our algorithm and show that our algorithm achieves the optimal query complexity for specific cases. In numerical experiments, we show that our method efficiently finds the optimal solution compared to some existing methods based on the pairwise comparison.

Suggested Citation

  • Kota Matsui & Wataru Kumagai & Takafumi Kanamori, 2017. "Parallel distributed block coordinate descent methods based on pairwise comparison oracle," Journal of Global Optimization, Springer, vol. 69(1), pages 1-21, September.
  • Handle: RePEc:spr:jglopt:v:69:y:2017:i:1:d:10.1007_s10898-016-0465-x
    DOI: 10.1007/s10898-016-0465-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0465-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10898-016-0465-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fuchang Gao & Lixing Han, 2012. "Implementing the Nelder-Mead simplex algorithm with adaptive parameters," Computational Optimization and Applications, Springer, vol. 51(1), pages 259-277, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Riva-Palacio, Alan & Leisen, Fabrizio, 2021. "Compound vectors of subordinators and their associated positive Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    2. Ivan Jericevich & Patrick Chang & Tim Gebbie, 2021. "Simulation and estimation of an agent-based market-model with a matching engine," Papers 2108.07806, arXiv.org, revised Aug 2021.
    3. Rocha Filho, T.M. & Moret, M.A. & Chow, C.C. & Phillips, J.C. & Cordeiro, A.J.A. & Scorza, F.A. & Almeida, A.-C.G. & Mendes, J.F.F., 2021. "A data-driven model for COVID-19 pandemic – Evolution of the attack rate and prognosis for Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Chang, Kuo-Hao, 2015. "A direct search method for unconstrained quantile-based simulation optimization," European Journal of Operational Research, Elsevier, vol. 246(2), pages 487-495.
    5. Ronan Keane & H. Oliver Gao, 2021. "Fast Calibration of Car-Following Models to Trajectory Data Using the Adjoint Method," Transportation Science, INFORMS, vol. 55(3), pages 592-615, May.
    6. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2021. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 73-100, June.
    7. Ralf Biehl, 2019. "Jscatter, a program for evaluation and analysis of experimental data," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-18, June.
    8. Mejía-de-Dios, Jesús-Adolfo & Mezura-Montes, Efrén & Toledo-Hernández, Porfirio, 2022. "Pseudo-feasible solutions in evolutionary bilevel optimization: Test problems and performance assessment," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    9. Papo, David & Righetti, Marco & Fadiga, Luciano & Biscarini, Fabio & Zanin, Massimiliano, 2020. "A minimal model of hospital patients’ dynamics in COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Pinto, Roberto, 2016. "Stock rationing under a profit satisficing objective," Omega, Elsevier, vol. 65(C), pages 55-68.
    11. Ingrida Steponavičė & Rob J. Hyndman & Kate Smith-Miles & Laura Villanova, 2017. "Dynamic algorithm selection for pareto optimal set approximation," Journal of Global Optimization, Springer, vol. 67(1), pages 263-282, January.
    12. Ferreiro, Ana M. & García-Rodríguez, José Antonio & Vázquez, Carlos & e Silva, E. Costa & Correia, A., 2019. "Parallel two-phase methods for global optimization on GPU," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 67-90.
    13. He, Jie-Cao & Hsieh, Chang-Chieh & Huang, Zi-Wei & Lin, Shih-Kuei, 2023. "Valuation of callable range accrual linked to CMS Spread under generalized swap market model," International Review of Financial Analysis, Elsevier, vol. 90(C).
    14. Carvajal-Rodríguez, A., 2020. "Multi-model inference of non-random mating from an information theoretic approach," Theoretical Population Biology, Elsevier, vol. 131(C), pages 38-53.
    15. Demirel, Duygun Fatih & Basak, Melek, 2019. "A fuzzy bi-level method for modeling age-specific migration," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).
    16. Vaninsky, Alexander, 2023. "Roadmapping green economic restructuring: A Ricardian gradient approach," Energy Economics, Elsevier, vol. 125(C).
    17. Liu, Yun & Heidari, Ali Asghar & Ye, Xiaojia & Liang, Guoxi & Chen, Huiling & He, Caitou, 2021. "Boosting slime mould algorithm for parameter identification of photovoltaic models," Energy, Elsevier, vol. 234(C).
    18. Lu Zhong & Mamadou Diagne & Qi Wang & Jianxi Gao, 2022. "Vaccination and three non-pharmaceutical interventions determine the dynamics of COVID-19 in the US," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-12, December.
    19. Dicks, Matthew & Paskaramoorthy, Andrew & Gebbie, Tim, 2024. "A simple learning agent interacting with an agent-based market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    20. Žiga Rojec & Tadej Tuma & Jernej Olenšek & Árpád Bűrmen & Janez Puhan, 2022. "Meta-Optimization of Dimension Adaptive Parameter Schema for Nelder–Mead Algorithm in High-Dimensional Problems," Mathematics, MDPI, vol. 10(13), pages 1-16, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:69:y:2017:i:1:d:10.1007_s10898-016-0465-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.