IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v194y2022i2d10.1007_s10957-022-02034-x.html
   My bibliography  Save this article

Simulated Annealing for Convex Optimization: Rigorous Complexity Analysis and Practical Perspectives

Author

Listed:
  • Riley Badenbroek

    (Erasmus University Rotterdam)

  • Etienne Klerk

    (Tilburg University)

Abstract

We give a rigorous complexity analysis of the simulated annealing algorithm by Kalai and Vempala (Math Oper Res 31(2):253–266, 2006) using the type of temperature update suggested by Abernethy and Hazan (International Conference on Machine Learning, 2016). The algorithm only assumes a membership oracle of the feasible set, and we prove that it returns a solution in polynomial time which is near-optimal with high probability. Moreover, we propose a number of modifications to improve the practical performance of this method, and present some numerical results for test problems from copositive programming.

Suggested Citation

  • Riley Badenbroek & Etienne Klerk, 2022. "Simulated Annealing for Convex Optimization: Rigorous Complexity Analysis and Practical Perspectives," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 465-491, August.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:2:d:10.1007_s10957-022-02034-x
    DOI: 10.1007/s10957-022-02034-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02034-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/s10957-022-02034-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. de Klerk, Etienne & Laurent, Monique, 2018. "Comparison of Lasserre's measure-based bounds for polynomial optimization to bounds obtained by simulated annealing," Other publications TiSEM 78f8f496-dc89-413e-864d-f, Tilburg University, School of Economics and Management.
    2. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    3. Etienne de Klerk & Monique Laurent, 2018. "Comparison of Lasserre’s Measure-Based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1317-1325, November.
    4. Badenbroek, Riley & de Klerk, Etienne, 2022. "Complexity analysis of a sampling-based interior point method for convex optimization," Other publications TiSEM 3d774c6d-8141-4f31-a621-5, Tilburg University, School of Economics and Management.
    5. Claude J. P. Bélisle & H. Edwin Romeijn & Robert L. Smith, 1993. "Hit-and-Run Algorithms for Generating Multivariate Distributions," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 255-266, May.
    6. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    7. Adam Tauman Kalai & Santosh Vempala, 2006. "Simulated Annealing for Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 253-266, May.
    8. Badenbroek, Riley, 2021. "Interior point methods and simulated annealing for nonsymmetric conic optimization," Other publications TiSEM 4374ab25-fdb5-4e6e-a198-6, Tilburg University, School of Economics and Management.
    9. Wei Xia & Juan C. Vera & Luis F. Zuluaga, 2020. "Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 40-56, 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. de Klerk, Etienne & Badenbroek, Riley, 2022. "Simulated annealing with hit-and-run for convex optimization: complexity analysis and practical perspectives," Other publications TiSEM 323b4588-65e0-4889-a555-9, Tilburg University, School of Economics and Management.
    2. Stephen Baumert & Archis Ghate & Seksan Kiatsupaibul & Yanfang Shen & Robert L. Smith & Zelda B. Zabinsky, 2009. "Discrete Hit-and-Run for Sampling Points from Arbitrary Distributions Over Subsets of Integer Hyperrectangles," Operations Research, INFORMS, vol. 57(3), pages 727-739, June.
    3. Badenbroek, Riley & de Klerk, Etienne, 2022. "Complexity analysis of a sampling-based interior point method for convex optimization," Other publications TiSEM 3d774c6d-8141-4f31-a621-5, Tilburg University, School of Economics and Management.
    4. Huseyin Mete & Yanfang Shen & Zelda Zabinsky & Seksan Kiatsupaibul & Robert Smith, 2011. "Pattern discrete and mixed Hit-and-Run for global optimization," Journal of Global Optimization, Springer, vol. 50(4), pages 597-627, August.
    5. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2024. "Randomized Control in Performance Analysis and Empirical Asset Pricing," Papers 2403.00009, arXiv.org.
    6. Etienne de Klerk & Monique Laurent, 2020. "Worst-Case Examples for Lasserre’s Measure–Based Hierarchy for Polynomial Optimization on the Hypercube," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 86-98, February.
    7. Luis V. Montiel & J. Eric Bickel, 2014. "A Generalized Sampling Approach for Multilinear Utility Functions Given Partial Preference Information," Decision Analysis, INFORMS, vol. 11(3), pages 147-170, September.
    8. Etienne de Klerk & Monique Laurent, 2018. "Comparison of Lasserre’s Measure-Based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1317-1325, November.
    9. Sorawit Saengkyongam & Anthony Hayter & Seksan Kiatsupaibul & Wei Liu, 2020. "Efficient computation of the stochastic behavior of partial sum processes," Computational Statistics, Springer, vol. 35(1), pages 343-358, March.
    10. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2023. "Randomized geometric tools for anomaly detection in stock markets," Post-Print hal-04223511, HAL.
    11. Bomze, Immanuel M. & Gabl, Markus, 2023. "Optimization under uncertainty and risk: Quadratic and copositive approaches," European Journal of Operational Research, Elsevier, vol. 310(2), pages 449-476.
    12. de Klerk, Etienne & Laurent, Monique, 2017. "Comparison of Lasserre's Measure-based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing," Other publications TiSEM 7a865ba0-bffb-43fb-a376-7, Tilburg University, School of Economics and Management.
    13. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2022. "Randomized geometric tools for anomaly detection in stock markets," Papers 2205.03852, arXiv.org, revised May 2022.
    14. Bélisle, Claude, 2000. "Slow hit-and-run sampling," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 33-43, March.
    15. de Klerk, Etienne & Laurent, Monique, 2018. "Comparison of Lasserre's measure-based bounds for polynomial optimization to bounds obtained by simulated annealing," Other publications TiSEM 78f8f496-dc89-413e-864d-f, Tilburg University, School of Economics and Management.
    16. Nabil Kahalé, 2019. "Efficient Simulation of High Dimensional Gaussian Vectors," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 58-73, February.
    17. Luis V. Montiel & J. Eric Bickel, 2013. "Approximating Joint Probability Distributions Given Partial Information," Decision Analysis, INFORMS, vol. 10(1), pages 26-41, March.
    18. Huseyin Onur Mete & Zelda B. Zabinsky, 2014. "Multiobjective Interacting Particle Algorithm for Global Optimization," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 500-513, August.
    19. Richard J. Caron & Tim Traynor & Shafiu Jibrin, 2010. "Feasibility and Constraint Analysis of Sets of Linear Matrix Inequalities," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 144-153, February.
    20. Tsionas, Mike G., 2020. "A coherent approach to Bayesian Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 281(2), pages 439-448.

    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:joptap:v:194:y:2022:i:2:d:10.1007_s10957-022-02034-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.