IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v57y2013i4p1193-1212.html
   My bibliography  Save this article

A modification of the DIRECT method for Lipschitz global optimization for a symmetric function

Author

Listed:
  • Ratko Grbić
  • Emmanuel Nyarko
  • Rudolf Scitovski

Abstract

In this paper, we consider a global optimization problem for a symmetric Lipschitz continuous function. An efficient modification of the well-known DIRECT (DIviding RECTangles) method called SymDIRECT is proposed for solving this problem. The method is illustrated and tested on several standard test functions. The application of this method to solving complex center-based clustering problems for the data having only one feature is particularly presented. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Ratko Grbić & Emmanuel Nyarko & Rudolf Scitovski, 2013. "A modification of the DIRECT method for Lipschitz global optimization for a symmetric function," Journal of Global Optimization, Springer, vol. 57(4), pages 1193-1212, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1193-1212
    DOI: 10.1007/s10898-012-0020-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-0020-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-0020-3?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. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
    2. Sanjo Zlobec, 2011. "Equivalent formulations of the gradient," Journal of Global Optimization, Springer, vol. 50(3), pages 549-553, July.
    3. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, September.
    4. Volkovich, Vladimir & Kogan, Jacob & Nicholas, Charles, 2007. "Building initial partitions through sampling techniques," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1097-1105, December.
    5. D. Serafino & G. Liuzzi & V. Piccialli & F. Riccio & G. Toraldo, 2011. "A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 175-190, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rudolf Scitovski & Snježana Majstorović & Kristian Sabo, 2021. "A combination of RANSAC and DBSCAN methods for solving the multiple geometrical object detection problem," Journal of Global Optimization, Springer, vol. 79(3), pages 669-686, March.
    2. Sabo, Kristian & Grahovac, Danijel & Scitovski, Rudolf, 2020. "Incremental method for multiple line detection problem — iterative reweighted approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 588-602.
    3. Donald R. Jones & Joaquim R. R. A. Martins, 2021. "The DIRECT algorithm: 25 years Later," Journal of Global Optimization, Springer, vol. 79(3), pages 521-566, March.
    4. Rudolf Scitovski, 2017. "A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set," Journal of Global Optimization, Springer, vol. 68(4), pages 713-727, August.
    5. Jonas Mockus & Remigijus Paulavičius & Dainius Rusakevičius & Dmitrij Šešok & Julius Žilinskas, 2017. "Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 425-450, January.
    6. Rudolf Scitovski & Kristian Sabo, 2021. "A combination of k-means and DBSCAN algorithm for solving the multiple generalized circle detection problem," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 83-98, March.
    7. Rudolf Scitovski & Kristian Sabo, 2019. "Application of the DIRECT algorithm to searching for an optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n and its application to the multiple circle detection problem," Journal of Global Optimization, Springer, vol. 74(1), pages 63-77, May.
    8. Qinghua Tao & Xiaolin Huang & Shuning Wang & Li Li, 2017. "Adaptive block coordinate DIRECT algorithm," Journal of Global Optimization, Springer, vol. 69(4), pages 797-822, December.
    9. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.

    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. Rudolf Scitovski, 2017. "A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set," Journal of Global Optimization, Springer, vol. 68(4), pages 713-727, August.
    2. Remigijus Paulavičius & Lakhdar Chiter & Julius Žilinskas, 2018. "Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants," Journal of Global Optimization, Springer, vol. 71(1), pages 5-20, May.
    3. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    4. Remigijus Paulavičius & Julius Žilinskas, 2014. "Simplicial Lipschitz optimization without the Lipschitz constant," Journal of Global Optimization, Springer, vol. 59(1), pages 23-40, May.
    5. Andrey Pepelyshev & Anatoly Zhigljavsky & Antanas Žilinskas, 2018. "Performance of global random search algorithms for large dimensions," Journal of Global Optimization, Springer, vol. 71(1), pages 57-71, May.
    6. Hajibaba, Homa & Gretzel, Ulrike & Leisch, Friedrich & Dolnicar, Sara, 2015. "Crisis-resistant tourists," Annals of Tourism Research, Elsevier, vol. 53(C), pages 46-60.
    7. 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.
    8. Robert Ferstl & David Seres, 2012. "Clustering Austrian Banks’ Business Models and Peer Groups in the European Banking Sector," Financial Stability Report, Oesterreichische Nationalbank (Austrian Central Bank), issue 24, pages 79-95.
    9. Jonathan Gillard & Anatoly Zhigljavsky, 2013. "Optimization challenges in the structured low rank approximation problem," Journal of Global Optimization, Springer, vol. 57(3), pages 733-751, November.
    10. Rios, Vicente & Gianmoena, Lisa, 2018. "Convergence in CO2 emissions: A spatial economic analysis with cross-country interactions," Energy Economics, Elsevier, vol. 75(C), pages 222-238.
    11. Rudolf Scitovski & Kristian Sabo, 2019. "Application of the DIRECT algorithm to searching for an optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n and its application to the multiple circle detection problem," Journal of Global Optimization, Springer, vol. 74(1), pages 63-77, May.
    12. Renato Bruni & Fabio Celani, 2019. "Combining Global and Local Strategies to Optimize Parameters in Magnetic Spacecraft Control via Attitude Feedback," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 997-1014, June.
    13. Boztug, Yasemin & Reutterer, Thomas, 2008. "A combined approach for segment-specific market basket analysis," European Journal of Operational Research, Elsevier, vol. 187(1), pages 294-312, May.
    14. Hornik, Kurt & Feinerer, Ingo & Kober, Martin & Buchta, Christian, 2012. "Spherical k-Means Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i10).
    15. Nazih-Eddine Belkacem & Lakhdar Chiter & Mohammed Louaked, 2024. "A Novel Approach to Enhance DIRECT -Type Algorithms for Hyper-Rectangle Identification," Mathematics, MDPI, vol. 12(2), pages 1-24, January.
    16. Francesco Dotto & Alessio Farcomeni & Luis Angel García-Escudero & Agustín Mayo-Iscar, 2017. "A fuzzy approach to robust regression clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 691-710, December.
    17. G. Liuzzi & S. Lucidi & V. Piccialli, 2016. "Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 449-475, November.
    18. C. J. Price & M. Reale & B. L. Robertson, 2021. "Oscars-ii: an algorithm for bound constrained global optimization," Journal of Global Optimization, Springer, vol. 79(1), pages 39-57, January.
    19. Sara Dolnicar & Friedrich Leisch, 2017. "Using segment level stability to select target segments in data-driven market segmentation studies," Marketing Letters, Springer, vol. 28(3), pages 423-436, September.
    20. Pierpaolo D'Urso & Girish Prayag & Marta Disegna & Riccardo Massari, 2013. "Market Segmentation using Bagged Fuzzy C–Means (BFCM): Destination Image of Western Europe among Chinese Travellers," BEMPS - Bozen Economics & Management Paper Series BEMPS13, Faculty of Economics and Management at the Free University of Bozen.

    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:57:y:2013:i:4:p:1193-1212. 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.