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A Generalized Conjugate Gradient Algorithm

Author

Listed:
  • S. Sanmatías

    (University of Valencia)

  • E. Vercher

    (University of Valencia)

Abstract

We present modifications of the generalized conjugate gradient algorithm of Liu and Storey for unconstrained optimization problems (Ref. 1), extending its applicability to situations where the search directions are not defined. The use of new search directions is proposed and one additional condition is imposed on the inexact line search. The convergence of the resulting algorithm can be established under standard conditions for a twice continuously differentiable function with a bounded level set. Algorithms based on these modifications have been tested on a number of problems, showing considerable improvements. Comparisons with the BFGS and other quasi-Newton methods are also given.

Suggested Citation

  • S. Sanmatías & E. Vercher, 1998. "A Generalized Conjugate Gradient Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 489-502, August.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:2:d:10.1023_a:1022653904717
    DOI: 10.1023/A:1022653904717
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    Cited by:

    1. Olivares, Alberto & Moguerza, Javier M. & Prieto, Francisco J., 2008. "Nonconvex optimization using negative curvature within a modified linesearch," European Journal of Operational Research, Elsevier, vol. 189(3), pages 706-722, September.
    2. Alberto Olivares & Javier Moguerza, 2009. "Improving directions of negative curvature in an efficient manner," Annals of Operations Research, Springer, vol. 166(1), pages 183-201, February.
    3. Javier Cano & Javier M. Moguerza & Francisco J. Prieto, 2017. "Using Improved Directions of Negative Curvature for the Solution of Bound-Constrained Nonconvex Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 474-499, August.

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