IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v155y2012i2d10.1007_s10957-012-0060-3.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0060-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-012-0060-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniela Lera & Yaroslav D. Sergeyev, 2018. "GOSH: derivative-free global optimization using multi-dimensional space-filling curves," Journal of Global Optimization, Springer, vol. 71(1), pages 193-211, May.
    2. A. Skjäl & T. Westerlund & R. Misener & C. A. Floudas, 2012. "A Generalization of the Classical αBB Convex Underestimation via Diagonal and Nondiagonal Quadratic Terms," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 462-490, August.
    3. Andreas Lundell & Anders Skjäl & Tapio Westerlund, 2013. "A reformulation framework for global optimization," Journal of Global Optimization, Springer, vol. 57(1), pages 115-141, September.
    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 Calvin & Gražina Gimbutienė & William O. Phillips & Antanas Žilinskas, 2018. "On convergence rate of a rectangular partition based global optimization algorithm," Journal of Global Optimization, Springer, vol. 71(1), pages 165-191, May.
    6. Antanas Žilinskas & James Calvin, 2019. "Bi-objective decision making in global optimization based on statistical models," Journal of Global Optimization, Springer, vol. 74(4), pages 599-609, August.
    7. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0060-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.