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

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  • 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
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    1. 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.
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    3. Sanjo Zlobec, 2011. "Equivalent formulations of the gradient," Journal of Global Optimization, Springer, vol. 50(3), pages 549-553, July.
    4. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, June.
    5. 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.
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    Cited by:

    1. Kristian Sabo & Rudolf Scitovski & Šime Ungar & Zoran Tomljanović, 2024. "A method for searching for a globally optimal k-partition of higher-dimensional datasets," Journal of Global Optimization, Springer, vol. 89(3), pages 633-653, July.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

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