IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v69y2017i4d10.1007_s10898-017-0544-7.html
   My bibliography  Save this article

On the convergence rate issues of general Markov search for global minimum

Author

Listed:
  • Dawid Tarłowski

    (Jagiellonian University)

Abstract

This paper focuses on the convergence rate problem of general Markov search for global minimum. Many of existing methods are designed for overcoming a very hard problem which is how to efficiently localize and approximate the global minimum of the multimodal function f while all information which can be used are the f-values evaluated for generated points. Because such methods use poor information on f, the following problem may occur: the closer to the optimum, the harder to generate a “better” (in sense of the cost function) state. This paper explores this issue on theoretical basis. To do so the concept of lazy convergence for a globally convergent method is introduced: a globally convergent method is called lazy if the probability of generating a better state from one step to another goes to zero with time. Such issue is the cause of very undesired convergence properties. This paper shows when an optimization method has to be lazy and the presented general results cover, in particular, the class of simulated annealing algorithms and monotone random search. Furthermore, some attention is put on accelerated random search and evolution strategies.

Suggested Citation

  • Dawid Tarłowski, 2017. "On the convergence rate issues of general Markov search for global minimum," Journal of Global Optimization, Springer, vol. 69(4), pages 869-888, December.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:4:d:10.1007_s10898-017-0544-7
    DOI: 10.1007/s10898-017-0544-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0544-7
    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/s10898-017-0544-7?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. Luis Rios & Nikolaos Sahinidis, 2013. "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, Springer, vol. 56(3), pages 1247-1293, July.
    2. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, June.
    3. M. Locatelli, 2001. "Convergence and first hitting time of simulated annealing algorithms for continuous global optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 171-199, December.
    4. Mathieu Gerber & Luke Bornn, 2017. "Improving simulated annealing through derandomization," Journal of Global Optimization, Springer, vol. 68(1), pages 189-217, May.
    5. R. L. Yang, 2000. "Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 691-716, March.
    6. Zheng Peng & Donghua Wu & Wenxing Zhu, 2016. "The robust constant and its applications in random global search for unconstrained global optimization," Journal of Global Optimization, Springer, vol. 64(3), pages 469-482, March.
    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. Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2018. "Metaheuristic vs. deterministic global optimization algorithms: The univariate case," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 245-259.
    2. Rubenthaler, Sylvain & Rydén, Tobias & Wiktorsson, Magnus, 2009. "Fast simulated annealing in with an application to maximum likelihood estimation in state-space models," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1912-1931, June.
    3. Weitao Sun & Yuan Dong, 2011. "Study of multiscale global optimization based on parameter space partition," Journal of Global Optimization, Springer, vol. 49(1), pages 149-172, January.
    4. Gerber, Mathieu & Bornn, Luke, 2018. "Convergence results for a class of time-varying simulated annealing algorithms," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1073-1094.
    5. Vasiliy V. Grigoriev & Petr N. Vabishchevich, 2021. "Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    6. Christophe Gouel & Nicolas Legrand, 2017. "Estimating the Competitive Storage Model with Trending Commodity Prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 744-763, June.
    7. Zhao, Jake, 2020. "Accounting for the corporate cash increase," European Economic Review, Elsevier, vol. 123(C).
    8. Breitmoser, Yves & Valasek, Justin, 2017. "A rationale for unanimity in committees," Discussion Papers, Research Unit: Economics of Change SP II 2017-308, WZB Berlin Social Science Center.
    9. Tavakol Aghaei, Vahid & Ağababaoğlu, Arda & Bawo, Biram & Naseradinmousavi, Peiman & Yıldırım, Sinan & Yeşilyurt, Serhat & Onat, Ahmet, 2023. "Energy optimization of wind turbines via a neural control policy based on reinforcement learning Markov chain Monte Carlo algorithm," Applied Energy, Elsevier, vol. 341(C).
    10. Pál, László & Sándor, Zsolt, 2023. "Comparing procedures for estimating random coefficient logit demand models with a special focus on obtaining global optima," International Journal of Industrial Organization, Elsevier, vol. 88(C).
    11. Qihong Feng & Kuankuan Wu & Jiyuan Zhang & Sen Wang & Xianmin Zhang & Daiyu Zhou & An Zhao, 2022. "Optimization of Well Control during Gas Flooding Using the Deep-LSTM-Based Proxy Model: A Case Study in the Baoshaceng Reservoir, Tarim, China," Energies, MDPI, vol. 15(7), pages 1-14, March.
    12. Luca Riboldi & Lars O. Nord, 2017. "Lifetime Assessment of Combined Cycles for Cogeneration of Power and Heat in Offshore Oil and Gas Installations," Energies, MDPI, vol. 10(6), pages 1-23, May.
    13. Khakifirooz, Marzieh & Fathi, Michel & Lee, I-Chen & Tseng, Sheng-Tsaing, 2023. "Neural ordinary differential equation for sequential optimal design of fatigue test under accelerated life test analysis," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    14. Gu, Ziyuan & Li, Yifan & Saberi, Meead & Rashidi, Taha H. & Liu, Zhiyuan, 2023. "Macroscopic parking dynamics and equitable pricing: Integrating trip-based modeling with simulation-based robust optimization," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 354-381.
    15. Khalid Mohammed Saffer Alzaidi & Oguz Bayat & Osman N. Uçan, 2018. "A Heuristic Approach for Optimal Planning and Operation of Distribution Systems," Journal of Optimization, Hindawi, vol. 2018, pages 1-19, June.
    16. Gandhi, Akhilesh & Zantye, Manali S. & Faruque Hasan, M.M., 2022. "Cryogenic energy storage: Standalone design, rigorous optimization and techno-economic analysis," Applied Energy, Elsevier, vol. 322(C).
    17. Cliff C Kerr & Salvador Dura-Bernal & Tomasz G Smolinski & George L Chadderdon & David P Wilson, 2018. "Optimization by Adaptive Stochastic Descent," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-16, March.
    18. G. R. Wood & D. W. Bulger & W. P. Baritompa & D. L. J. Alexander, 2006. "Backtracking Adaptive Search: Distribution of Number of Iterations to Convergence," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 547-562, March.
    19. Marc Robini & Pierre-Jean Reissman, 2013. "From simulated annealing to stochastic continuation: a new trend in combinatorial optimization," Journal of Global Optimization, Springer, vol. 56(1), pages 185-215, May.
    20. Vikse, Matias & Watson, Harry A.J. & Kim, Donghoi & Barton, Paul I. & Gundersen, Truls, 2020. "Optimization of a dual mixed refrigerant process using a nonsmooth approach," Energy, Elsevier, vol. 196(C).

    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:4:d:10.1007_s10898-017-0544-7. 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.