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On Dealing with Minima at the Border of a Simplicial Feasible Area in Simplicial Branch and Bound

Author

Listed:
  • Boglárka G.-Tóth

    (University of Szeged)

  • Eligius M. T. Hendrix

    (Universidad de Málaga
    Wageningen University)

  • Leocadio G. Casado

    (University of Almería, CeiA3)

  • Frédéric Messine

    (University of Toulouse)

Abstract

We consider a simplicial branch and bound Global Optimization algorithm, where the search region is a simplex. Apart from using longest edge bisection, a simplicial partition set can be reduced due to monotonicity of the objective function. If there is a direction in which the objective function is monotone over a simplex, depending on whether the facets that may contain the minimum are at the border of the search region, we can remove the simplex completely, or reduce it to some of its border facets. Our research question deals with finding monotone directions and labeling facets of a simplex as border after longest edge bisection and reduction due to monotonicity. Experimental results are shown over a set of global optimization problems where the feasible set is defined as a simplex, and a global minimum point is located at a face of the simplicial feasible area.

Suggested Citation

  • Boglárka G.-Tóth & Eligius M. T. Hendrix & Leocadio G. Casado & Frédéric Messine, 2024. "On Dealing with Minima at the Border of a Simplicial Feasible Area in Simplicial Branch and Bound," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1880-1909, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02480-9
    DOI: 10.1007/s10957-024-02480-9
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    References listed on IDEAS

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    1. de Klerk, E., 2008. "The complexity of optimizing over a simplex, hypercube or sphere : A short survey," Other publications TiSEM 485b6860-cf1d-4cad-97b8-2, Tilburg University, School of Economics and Management.
    2. B. G.-Tóth & L. G. Casado & E. M. T. Hendrix & F. Messine, 2021. "On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic," Journal of Global Optimization, Springer, vol. 80(4), pages 779-804, August.
    3. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 111-125, June.
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