Skip to main content

The Langevin Equation as a Global Minimization Algorithm

  • Conference paper

Part of the book series: NATO ASI Series ((NATO ASI F,volume 20))

Abstract

During the past two years a great deal of attention has been given to simulated annealing as a global minimization algorithm in combinatorial optimization problems [11], image processing problems [2], and other problems [9]. The first rigorous result concerning the convergence of the annealing algorithm was obtained in [2]. In [4], the annealing algorithm was treated as a special case of non-stationary Markov chains, and some optimal convergence estimates and an ergodic theorem were established. Optimal estimates for the annealing algorithm have recently been obtained by nice intuitive arguments in [7].

Partially supported by NSF Grant MCS-8301864.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dixon, L.C.W., and G.P. Szegö (eds.): Towards Global Optimization 2, North-Holland, (1978).

    Google Scholar 

  2. Geman, S. and D. Geman: “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images”, IEEE transactions, PAMI 6(1984), 721–741.

    Article  MATH  Google Scholar 

  3. Geman, S. and C.R. Huang: “Diffusions for Global Optimization”, preprint, 1984.

    Google Scholar 

  4. Gidas, B.: “Non-Stationary Markov Chains and Convergence of the Ánnealing Algorithm”, J. Stat. Phys. 39 (1985), 73–131.

    Article  MATH  MathSciNet  Google Scholar 

  5. Gidas, B.: “Global Minimization via the Langevin Equation” in preparation.

    Google Scholar 

  6. Grenander, U.: Tutorial in Pattern Theory, Brown University, (1983).

    Google Scholar 

  7. Hajek, B.: “Cooling Schedules for Optimal Annealing”, preprint, 1985.

    Google Scholar 

  8. Helffer, B. and I. Sjöstrand: “Puits Multiples en Mecanique Semi-Classique IV, Etude du Complexe de Witten”, preprint, 1984.

    Google Scholar 

  9. Hinton, G., T. Sejnowski, and D. Ackley: “Boltzmann Machine: Constraint Satisfaction Networks that Learn”., preprint, 1984.

    Google Scholar 

  10. Kan, A., C. Boender, and G. Timmer: “A Stochastic Approach to Global Optimization”, preprint, 1984.

    Google Scholar 

  11. Kirkpatrick, S., CD. Gelatt, and M. Vecchi: “Optimization by Simulated Annealing”, Science 220, 13 May (1983) 621–680.

    MathSciNet  Google Scholar 

  12. Metropolis, N., et. al.: “Equations of State Calculations by Past Computing Machines”, J. Chem. Phys. 21 (1953), 1087–1091.

    Article  Google Scholar 

  13. Parisi, G.: “Prolegomena To any Further Computer Evaluation of the QCD Mass Spectrum”, in Progress in Gauge Field Theory Cargese (1983).

    Google Scholar 

  14. Simon, B.: “Semiclassical Analysis of Low Lying Eigenvalues I. Non-degenerate Minima: Asymptotic Expansions”, Ann. Inst. Henri Poincaré 38 (1983), 295–307.

    MATH  Google Scholar 

  15. Witten, E.: “Supersymmetry and Morse Theory”, J. Diff. Geometry 17 (1982), 661–692.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gidas, B. (1986). The Langevin Equation as a Global Minimization Algorithm. In: Bienenstock, E., Soulié, F.F., Weisbuch, G. (eds) Disordered Systems and Biological Organization. NATO ASI Series, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82657-3_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-82657-3_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82659-7

  • Online ISBN: 978-3-642-82657-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics