Advertisement

Global maxima of real-valued functions

  • G. Gabrielsen
Contributed Papers

Abstract

In this paper, sufficient conditions for a local maximum to be global are discussed. The result is that a real continuously differentiable functionf, defined on a subset ofRn, under fairly weak conditions, is unimodal iff has a strict local maximum at any stationary point.

Key Words

Global optimality strict local maxima elementary topology differentiability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Copas, J. B.,On the Unimodality of the Likelihood for the Cauchy Distribution, Biometrika, Vol. 62, pp. 701–704, 1975.Google Scholar
  2. 2.
    Huzurbazar, V. S.,On a Property of Distributions Admitting Sufficient Statistics, Biometrika, Vol. 36, pp. 71–74, 1949.Google Scholar
  3. 3.
    Kendall, M. G., andStuart, A.,The Advanced Theory of Statistics, Vol. 2, Charles Griffin and Company, London, England, 1961.Google Scholar
  4. 4.
    Bury, K. V.,Statistical Models in Applied Science, John Wiley and Sons, New York, New York, 1974.Google Scholar
  5. 5.
    Zang, I., andAvriel, M.,On Functions Whose Local Minima Are Global, Journal of Optimization Theory and Applications, Vol. 16, pp. 183–190, 1975.Google Scholar
  6. 6.
    Barndorff-Nielsen, O., andBlæsild, P.,Global Maxima and Likelihood in Linear Models, University of Aarhus, Institute of Mathematics, Research Report No. 57, 1980.Google Scholar
  7. 7.
    Willard, S.,General Topology, Addison-Wesley, Reading, Massachusetts, 1970.Google Scholar
  8. 8.
    Courant, R.,Differential and Integral Calculus, Vol. 2, Blackie and Son, London, England, 1966.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • G. Gabrielsen
    • 1
  1. 1.Institute of Theoretical Statistics, Copenhagen School of Economics and Business AdministrationCopenhagenDenmark

Personalised recommendations