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An information global minimization algorithm using the local improvement technique

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Abstract

In this paper, the global optimization problem with a multiextremal objective function satisfying the Lipschitz condition over a hypercube is considered. An algorithm that belongs to the class of information methods introduced by R.G. Strongin is proposed. The knowledge of the Lipschitz constant is not supposed. The local tuning on the behavior of the objective function and a new technique, named the local improvement, are used in order to accelerate the search. Two methods are presented: the first one deals with the one-dimensional problems and the second with the multidimensional ones (by using Peano-type space-filling curves for reduction of the dimension of the problem). Convergence conditions for both algorithms are given. Numerical experiments executed on more than 600 functions show quite a promising performance of the new techniques.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, Italy

    Daniela Lera

  2. Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria and the Institute of High Performance Computing and Networking of the National Research Council of Italy, Via Pietro Bucci 42C, 87036, Rende, CS, Italy

    Yaroslav D. Sergeyev

  3. Software Department, University of Nizhni Novgorod, Gagarin Av. 23, Nizhni Novgorod, Russia

    Yaroslav D. Sergeyev

Authors
  1. Daniela Lera
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  2. Yaroslav D. Sergeyev
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Corresponding author

Correspondence to Yaroslav D. Sergeyev.

Additional information

This research was supported by the following grants: Italian PRIN project 2007-9PLLN7, Russian RFBR grant 07-01-00467-a, the Russian Federal Program “Scientists and Educators in Russia of Innovations”, contract number 02.740.11.5018, and the grant 4694.2008.9 for supporting the leading research groups awarded by the President of the Russian Federation.

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Lera, D., Sergeyev, Y.D. An information global minimization algorithm using the local improvement technique. J Glob Optim 48, 99–112 (2010). https://doi.org/10.1007/s10898-009-9508-x

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  • DOI: https://doi.org/10.1007/s10898-009-9508-x

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