Advertisement

Journal of Optimization Theory and Applications

, Volume 107, Issue 2, pp 261–274 | Cite as

Frame Based Methods for Unconstrained Optimization

  • I. D. Coope
  • C. J. Price
Article

Abstract

This paper describes a wide class of direct search methods for unconstrained optimization, which make use of fragments of grids called frames. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.

derivative free optimization positive basis methods convergence analysis frame based methods 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lewis, R. M., and Torczon, V., Rank Ordering and Positive Bases in Pattern Search Algorithms, SIAM Journal on Optimization.Google Scholar
  2. 2.
    Torczon, V., On the Convergence of Pattern Search Algorithms, SIAM Journal on Optimization, Vol. 7, pp. 1–25, 1997.Google Scholar
  3. 3.
    Torczon, V., On the Convergence of the Multidirectional Search Algorithm, SIAM Journal on Optimization, Vol. 1, pp. 123–145, 1991.Google Scholar
  4. 4.
    Dennis, J. E., and Torczon, V., Direct Search Methods on Parallel Machines, SIAM Journal on Optimization, Vol. 1, pp. 448–474, 1991.Google Scholar
  5. 5.
    Coope, I. D., and Price, C. J., On the Convergence of Grid-Based Methods for Unconstrained Minimization, Research Report 180, Department of Mathematics, University of Canterbury, Christchurch, New Zealand.Google Scholar
  6. 6.
    Coope, I. D., and Price, C. J., Convergent Frame-Based Quasi-Newton Methods (to appear).Google Scholar
  7. 7.
    Conn, A., Scheinberg, K., and Toint, P. L., On the Convergence of Derivative-Free Methods for Unconstrained Optimization, Approximation Theory and Optimization, Edited by M. D. Buhmann and A. Iserles, Cambridge University Press, Cambridge, England, pp. 83–108, 1997.Google Scholar
  8. 8.
    Powell, M. J. D., Direct Search Algorithms for Optimization Calculations, Acta Numerica, Vol. 7, pp. 287–336, 1998.Google Scholar
  9. 9.
    Davis, C., Theory of Positive Linear Dependence, American Journal of Mathematics, Vol. 76, pp. 733–746, 1954.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • I. D. Coope
    • 1
  • C. J. Price
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand
  2. 2.Department of Mathematics and StatisticsUniversity of CanterburyChristchurch

Personalised recommendations