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On a Global Optimization Algorithm for Bivariate Smooth Functions

Author

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  • James M. Calvin

    (New Jersey Institute of Technology)

  • Antanas Žilinskas

    (Vilnius University)

Abstract

The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided.

Suggested Citation

  • James M. Calvin & Antanas Žilinskas, 2014. "On a Global Optimization Algorithm for Bivariate Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 528-547, November.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-014-0531-9
    DOI: 10.1007/s10957-014-0531-9
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    References listed on IDEAS

    as
    1. J. Calvin & A. Žilinskas, 2000. "One-Dimensional P-Algorithm with Convergence Rate O(n−3+δ) for Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 297-307, August.
    2. Giampaolo Liuzzi & Stefano Lucidi & Veronica Piccialli, 2010. "A partition-based global optimization algorithm," Journal of Global Optimization, Springer, vol. 48(1), pages 113-128, September.
    3. James M. Calvin & Yvonne Chen & Antanas Žilinskas, 2012. "An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 628-636, November.
    4. Hendrix, Eligius M.T. & Casado, Leocadio G. & Garcí­a, Inmaculada, 2008. "The semi-continuous quadratic mixture design problem: Description and branch-and-bound approach," European Journal of Operational Research, Elsevier, vol. 191(3), pages 803-815, December.
    5. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, June.
    Full references (including those not matched with items on IDEAS)

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