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Efficient Strategy for Adaptive Partition of N-Dimensional Intervals in the Framework of Diagonal Algorithms

Author

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  • YA. D. Sergeyev

    (University of Calabria, Rende
    University of Nizhni Novgorod)

Abstract

In this paper, the problem of the minimal description of the structure offunctional f(x) over an N-dimensional interval is considered. Thedescription is obtained by applying diagonal algorithms, i.e., proceduressequentially partitioning the given hyperinterval and evaluating f(x)at the vertices corresponding to the main diagonal of each generatedsubinterval. Two partition strategies traditionally used for solving thisproblem are analyzed and it is demonstrated that using them can result ina high number of redundant evaluations of the functional f(x). Anew efficient partition strategy is proposed; it reduces considerably thenumber of evaluations of f(x) and the memory complexity.

Suggested Citation

  • YA. D. Sergeyev, 2000. "Efficient Strategy for Adaptive Partition of N-Dimensional Intervals in the Framework of Diagonal Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 145-168, October.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:1:d:10.1023_a:1004613001755
    DOI: 10.1023/A:1004613001755
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    References listed on IDEAS

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    1. Csendes, Tibor & Pinter, Janos, 1993. "The impact of accelerating tools on the interval subdivision algorithm for global optimization," European Journal of Operational Research, Elsevier, vol. 65(3), pages 314-320, March.
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    Cited by:

    1. Albertas Gimbutas & Antanas Žilinskas, 2018. "An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section," Journal of Global Optimization, Springer, vol. 71(1), pages 115-127, May.
    2. Ya. D. Sergeyev, 2005. "Efficient Partition of N-Dimensional Intervals in the Framework of One-Point-Based Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 503-510, February.
    3. 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.
    4. 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.
    5. 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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