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

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Jones, Donald R.; Martins, Joaquim R. R. A.: The DIRECT algorithm: 25 years later (2021)
  2. Scitovski, Rudolf; Majstorović, Snježana; Sabo, Kristian: A combination of \textttRANSACand \textttDBSCANmethods for solving the multiple geometrical object detection problem (2021)
  3. Scitovski, Rudolf; Sabo, Kristian: A combination of (k)-means and \textttDBSCANalgorithm for solving the multiple generalized circle detection problem (2021)
  4. Sabo, Kristian; Grahovac, Danijel; Scitovski, Rudolf: Incremental method for multiple line detection problem -- iterative reweighted approach (2020)
  5. Scitovski, Rudolf; Sabo, Kristian: The adaptation of the (k)-means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm. (2019)
  6. Scitovski, Rudolf; Sabo, Kristian: Application of the \textttDIRECTalgorithm to searching for an optimal (k)-partition of the set (\mathcalA\subset\mathbbR^n) and its application to the multiple circle detection problem (2019)
  7. Akman, Devin; Akman, Olcay; Schaefer, Elsa: Parameter estimation in ordinary differential equations modeling via particle swarm optimization (2018)
  8. Scitovski, Rudolf; Sušac, Marijana Zekić; Has, Adela: Searching for an optimal partition of incomplete data with application in modeling energy efficiency of public buildings (2018)
  9. Mockus, Jonas; Paulavičius, Remigijus; Rusakevičius, Dainius; Šešok, Dmitrij; Žilinskas, Julius: Application of reduced-set Pareto-Lipschitzian optimization to truss optimization (2017)
  10. Scitovski, Rudolf: 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 (2017)
  11. Tao, Qinghua; Huang, Xiaolin; Wang, Shuning; Li, Li: Adaptive block coordinate DIRECT algorithm (2017)
  12. Turkalj, Željko; Markulak, Damir; Singer, Slavica; Scitovski, Rudolf: Research project grouping and ranking by using adaptive Mahalanobis clustering (2016)
  13. Paulavičius, Remigijus; Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Žilinskas, Julius: Globally-biased disimpl algorithm for expensive global optimization (2014)
  14. Paulavičius, Remigijus; Žilinskas, Julius: Simplicial Lipschitz optimization without the Lipschitz constant (2014)
  15. Sabo, Kristian: Center-based (l_1)-clustering method (2014)
  16. Sabo, Kristian; Scitovski, Rudolf: Interpretation and optimization of the (k)-means algorithm. (2014)
  17. Grbić, Ratko; Nyarko, Emmanuel Karlo; Scitovski, Rudolf: A modification of the \textttDIRECTmethod for Lipschitz global optimization for a symmetric function (2013)