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Frame-Based Ray Search Algorithms in Unconstrained Optimization

Author

Listed:
  • C.J. Price

    (University of Canterbury)

  • I.D. Coope

    (University of Canterbury)

Abstract

This paper describes a class of frame-based direct search methods for unconstrained optimization without derivatives. A template for convergent direct search methods is developed, some requiring only the relative ordering of function values. At each iteration, the template considers a number of search steps which form a positive basis and conducts a ray search along a step giving adequate decrease. Various ray search strategies are possible, including discrete equivalents of the Goldstein–Armijo and one-sided Wolfe–Powell ray searches. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.

Suggested Citation

  • C.J. Price & I.D. Coope, 2003. "Frame-Based Ray Search Algorithms in Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 359-377, February.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:2:d:10.1023_a:1022414105888
    DOI: 10.1023/A:1022414105888
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    References listed on IDEAS

    as
    1. C.J. Price & I.D. Coope & D. Byatt, 2002. "A Convergent Variant of the Nelder–Mead Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 5-19, April.
    2. I. D. Coope & C. J. Price, 2000. "Frame Based Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 261-274, November.
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