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An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions

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  • James M. Calvin

    (New Jersey Institute of Technology)

  • Yvonne Chen

    (New Jersey Institute of Technology)

  • Antanas Žilinskas

    (Vilnius University)

Abstract

We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a twice continuously differentiable function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0060-3
    DOI: 10.1007/s10957-012-0060-3
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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. Daniela Lera & Yaroslav Sergeyev, 2010. "An information global minimization algorithm using the local improvement technique," Journal of Global Optimization, Springer, vol. 48(1), pages 99-112, September.
    3. Christodoulos A. Floudas & Vladik Kreinovich, 2007. "Towards Optimal Techniques for Solving Global Optimization Problems: Symmetry-Based Approach," Springer Optimization and Its Applications, in: Aimo Törn & Julius Žilinskas (ed.), Models and Algorithms for Global Optimization, pages 21-42, Springer.
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    Citations

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    Cited by:

    1. Sergeyev, Yaroslav D. & Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2017. "Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 96-109.
    2. Jia Hao & Mengying Zhou & Guoxin Wang & Liangyue Jia & Yan Yan, 2020. "Design optimization by integrating limited simulation data and shape engineering knowledge with Bayesian optimization (BO-DK4DO)," Journal of Intelligent Manufacturing, Springer, vol. 31(8), pages 2049-2067, December.
    3. Lera, Daniela & Posypkin, Mikhail & Sergeyev, Yaroslav D., 2021. "Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Yaroslav D. Sergeyev & Marat S. Mukhametzhanov & Dmitri E. Kvasov & Daniela Lera, 2016. "Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 186-208, October.
    5. 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.

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