Skip to main content
SpringerLink
Log in

Uniform convergence for moment problems with Fermi-Dirac type entropies

  • Articles
  • Published:
Zeitschrift für Operations Research Aims and scope Submit manuscript

Abstract

We consider the best entropic estimation to a unknown density¯x, given some of its algebraic or trigonometric moments. A uniform convergence theorem is established in this paper for such problems using Fermi-Dirac type entropic objectives.

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. Borwein JM, Lewis AS (1991) Convergence of best entropy estimates. SIAM J Optim 1(2):191–205

    Google Scholar 

  2. Borwein JM, Lewis AS (1991) Duality relationships for entropy-like minimization problems. SIAM Journal of Control Theory and Optimization 29(2):325–338

    Google Scholar 

  3. Borwein JM, Lewis AS (1991) On the convergence of moment problems. Trans of Amer Math Soc 325(1):249–271

    Google Scholar 

  4. Borwein JM, Lewis AS (1993) A survey of convergence results for maximum entropy methods, 39–48. In: Mohammad-Djafari A, Demoments G (Ed) Maximum entropy and Bayesian Methods Kluwer Dordrecht

    Google Scholar 

  5. Borwein JM, Lewis AS (1992) Strong rotundity and optimization. SIAM J on Optimization (accepted)

  6. Borwein P, Lewis AS Moment-matching and best entropy estimation. J of Mathematical Analysis and Applications (submitted)

  7. Forte B, Hughes W, Pales Z (1989) Maximum entropy estimators and the problem of moments. Rendiconti di Mathematica Serie VII, 9:689–699

    Google Scholar 

  8. Huang W (1993) Linearly constrained convex programming of entropy type: Convergence and algorithms. PhD thesis Dalhousie University Canada

    Google Scholar 

  9. Lewis AS (1992) The convergence of Burg and other entropy estimates. Technical Report CORR 92-08

  10. Mead LR, Papanicolaou N (1984) Maximum entropy in the problem of moments. J Math Phys 25:2404–2417

    Google Scholar 

  11. Rockafellar RT (1970) Convex analysis. Princeton University Press

  12. Teboulle M, Vajda I (1992) Convergence of bestø-entropy estimates. IEEE Transactions on Information Theory (to appear)

  13. Telyakovskii SA (1990) Research in the theory of approxmation of functions at the Mathematical Institute of the Academy of Sciences. Proceedings of the Steklov Institute of Mathematics 1

  14. Visintin A (1984) Strong convergence results related to strict convexity. Communications on Partial Differential Equations 9:439–466

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, British Columbia, USA

    J. M. Borwein

  2. Department of Mathematics and Sciences, Lakehead University, P7B 5E1, Thunder Bay, Ontario, USA

    W. Huang

Authors
  1. J. M. Borwein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borwein, J.M., Huang, W. Uniform convergence for moment problems with Fermi-Dirac type entropies. ZOR - Methods and Models of Operations Research 40, 239–252 (1994). https://doi.org/10.1007/BF01432968

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01432968

Key words

Search

Navigation