Zeitschrift für Operations Research

, Volume 40, Issue 3, pp 239–252 | Cite as

Uniform convergence for moment problems with Fermi-Dirac type entropies

  • J. M. Borwein
  • W. Huang


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.

Key words

linear constrained optimization moment problems uniform convergence best approximation Fermi-Dirac entropy Fenchel duality 


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  1. [1]
    Borwein JM, Lewis AS (1991) Convergence of best entropy estimates. SIAM J Optim 1(2):191–205Google Scholar
  2. [2]
    Borwein JM, Lewis AS (1991) Duality relationships for entropy-like minimization problems. SIAM Journal of Control Theory and Optimization 29(2):325–338Google Scholar
  3. [3]
    Borwein JM, Lewis AS (1991) On the convergence of moment problems. Trans of Amer Math Soc 325(1):249–271Google Scholar
  4. [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 DordrechtGoogle Scholar
  5. [5]
    Borwein JM, Lewis AS (1992) Strong rotundity and optimization. SIAM J on Optimization (accepted)Google Scholar
  6. [6]
    Borwein P, Lewis AS Moment-matching and best entropy estimation. J of Mathematical Analysis and Applications (submitted)Google Scholar
  7. [7]
    Forte B, Hughes W, Pales Z (1989) Maximum entropy estimators and the problem of moments. Rendiconti di Mathematica Serie VII, 9:689–699Google Scholar
  8. [8]
    Huang W (1993) Linearly constrained convex programming of entropy type: Convergence and algorithms. PhD thesis Dalhousie University CanadaGoogle Scholar
  9. [9]
    Lewis AS (1992) The convergence of Burg and other entropy estimates. Technical Report CORR 92-08Google Scholar
  10. [10]
    Mead LR, Papanicolaou N (1984) Maximum entropy in the problem of moments. J Math Phys 25:2404–2417Google Scholar
  11. [11]
    Rockafellar RT (1970) Convex analysis. Princeton University PressGoogle Scholar
  12. [12]
    Teboulle M, Vajda I (1992) Convergence of bestø-entropy estimates. IEEE Transactions on Information Theory (to appear)Google Scholar
  13. [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 1Google Scholar
  14. [14]
    Visintin A (1984) Strong convergence results related to strict convexity. Communications on Partial Differential Equations 9:439–466Google Scholar

Copyright information

© Physica-Verlag 1994

Authors and Affiliations

  • J. M. Borwein
    • 1
  • W. Huang
    • 2
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyUSA
  2. 2.Department of Mathematics and SciencesLakehead UniversityThunder BayUSA

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