Skip to main content
SpringerLink
Log in

A lower bound on convergence rates of nonadaptive algorithms for univariate optimization with noise

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

This paper considers complexity bounds for the problem of approximating the global minimum of a univariate function when the function evaluations are corrupted by random noise. We take an average-case point of view, where the objective function is taken to be a sample function of a Wiener process and the noise is independent Gaussian. Previous papers have bounded the convergence rates of some nonadaptive algorithms. We establish a lower bound on the convergence rate of any nonadaptive algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Al-Mharmah H., Calvin J.: Optimal random nonadaptive algorithm for global optimization of Brownian motion. J. Glob. Optim. 8, 81–90 (1996)

    Article  Google Scholar 

  2. Al-Mharmah H., Calvin J.: Comparison of one-dimensional composite and non-composite passive algorithms. J. Glob. Optim. 15, 169–180 (1999)

    Article  Google Scholar 

  3. Calvin J.M.: Average performance of passive algorithms for global optimization of Brownian motion. J. Math. Anal. Appl. 191, 608–617 (1995)

    Article  Google Scholar 

  4. Calvin J.M.: Nonadaptive univariate optimization for observations with noise. In: Törn, A., Zilinskas, J. (eds) Models and Algorithms for Global Optimization, pp. 185–192. Springer, New York (2007)

    Chapter  Google Scholar 

  5. Calvin J.M., Z̆ilinskas A.: One-dimensional global optimization for observations with noise. Comput. Math. Appl. 50, 157–169 (2005)

    Article  Google Scholar 

  6. Kushner H.: A versatile stochastic model of a function of unknown and time-varying form. J. Math. Anal. Appl. 5, 150–167 (1962)

    Article  Google Scholar 

  7. Kushner H.: A new method of locating the maximum point of a multipeak curve in the presence of noise. J. Basic Eng. 86, 97–106 (1964)

    Google Scholar 

  8. Plaskota L.: Noisy Information and Computational Complexity. Cambridge University Press, Cambridge (1996)

    Book  Google Scholar 

  9. Revuz D., Yor M.: Continuous Martingales and Brownian Motion. Springer-Verlag, Berlin Heidelberg (1991)

    Google Scholar 

  10. Ritter K.: Approximation and optimization on the Wiener space. J. Complex. 6, 337–364 (1990)

    Article  Google Scholar 

  11. Strongin R.: Information method for multiextremal minimization with noisy observations. Trans. USSR Acad. Sci. Eng. Cybern. 6, 116–126 (1969)

    Google Scholar 

  12. Strongin R., Sergeyev Y.: Global Optimization with Non-Convex Constraints. Kluwer, Dordrecht (2000)

    Google Scholar 

  13. Törn A., Z̆ilinskas A.: Global Optimization. Lecture Notes in Computer Science, Vol. 350. Springer-Verlag, Berlin (1989)

    Google Scholar 

  14. Z̆ilinskas A.: Two algorithms for one-dimensional multimodal minimization. Math. Oper. Stat. ser. Optim. 12, 53–63 (1981)

    Google Scholar 

  15. Z̆ilinskas A.: Axiomatic characterization of a global optimization algorithm and investigation of its search strategies. Oper. Res. Lett. 4, 35–39 (1985)

    Article  Google Scholar 

  16. Zhigljavsky A., Z̆ilinskas A.: Stochastic Global Optimization. Springer, New york (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, 07102-1982, USA

    James M. Calvin

Authors
  1. James M. Calvin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James M. Calvin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Calvin, J.M. A lower bound on convergence rates of nonadaptive algorithms for univariate optimization with noise. J Glob Optim 48, 17–27 (2010). https://doi.org/10.1007/s10898-010-9530-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-010-9530-z

Keywords

Search

Navigation