Skip to main content
SpringerLink
Log in

An adaptive stochastic global optimization algorithm for one-dimensional functions

  • Global Optimization
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In this paper a new algorithm is proposed, based upon the idea of modeling the objective function of a global optimization problem as a sample path from a Wiener process. Unlike previous work in this field, in the proposed model the parameter of the Wiener process is considered as a random variable whose conditional (posterior) distribution function is updated on-line. Stopping criteria for Bayesian algorithms are discussed and detailed proofs on finite-time stopping are provided.

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. M. Abramowitz and I.A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1972).

    Google Scholar 

  2. J.O. Berger,Statistical Decisions Theory and Bayesian Analysis, 2nd ed., Springer Series in Statistics (Springer, New York, 1985).

    Google Scholar 

  3. B. Betrò, Bayesian methods in global optimization, J. Global Optim. 1(1991)1–14.

    Article  Google Scholar 

  4. P. Hansen, B. Jaumard and S.-H. Lu, Global optimization of univariate Lipschitz functions: Survey and properties, Math. Progr. 55(1992)251–272.

    Article  Google Scholar 

  5. M. Locatelli, Algoritmi Bayesiani per l'ottimizzazione globale, unpublished laurea thesis (1992).

  6. J. Mockus, On Bayesian methods of optimization, in:Towards Global Optimization, ed. L.C.W. Dixon and G.P. Szegö (North-Holland, Amsterdam, 1975).

    Google Scholar 

  7. J. Mockus,Bayesian Approach to Global Optimization, Mathematics and Its Applications (Soviet Series) (Kluwer Academic, Dordrecht, 1989).

    Google Scholar 

  8. A.H.G. Rinnooy Kan and G.T. Timmer, Global optimization, in:Optimization, ed. G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J. Todd, Handbooks in Operations Research and Management Science (North-Holland, 1989) pp. 631–662.

  9. F. Schoen, Stochastic techniques for global optimization: a survey of recent advances, J. Global Optim. 1(1991)207–228.

    Article  Google Scholar 

  10. R.G. Strongin, Algorithms for multi-extremal mathematical programming problems employing the set of joint space-filling curves, J. Global Optim. 2(1992)357–378.

    Article  Google Scholar 

  11. A. Törn and A. Zilinskas,Global Optimization, Lecture Notes in Computer Sciences (Springer, Berlin, 1989).

    Google Scholar 

  12. S. Wolfram,Mathematical — A System for Doing Mathematics by Computer (Addison-Wesley, 1991).

  13. A.A. Zhigljavsky,Theory of Global Random Search, Mathematics and its Applications (Soviet Series) (Kluwer Academic, Dordrecht, 1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dip. Scienze dell'Informazione, Università di Milano, via Comelico 39/41, Milano, Italy

    Marco Locatelli

  2. Dip. Sistemi e Informatica, Università di Firenze, via di Santa Marta 3, I-50139, Firenze, Italy

    Fabio Schoen

Authors
  1. Marco Locatelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabio Schoen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research has been partially supported by “Progetto MURST 40% Metodi di Ottimizzazione per le Decisioni”.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Locatelli, M., Schoen, F. An adaptive stochastic global optimization algorithm for one-dimensional functions. Ann Oper Res 58, 261–278 (1995). https://doi.org/10.1007/BF02096402

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096402

Keywords

Search

Navigation