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Numerical Experience with a Class of Self-Scaling Quasi-Newton Algorithms

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  • M. Al-Baali

    (UAE University)

Abstract

Self-scaling quasi-Newton methods for unconstrained optimization depend upon updating the Hessian approximation by a formula which depends on two parameters (say, τ and θ) such that τ = 1, θ = 0, and θ = 1 yield the unscaled Broyden family, the BFGS update, and the DFP update, respectively. In previous work, conditions were obtained on these parameters that imply global and superlinear convergence for self-scaling methods on convex objective functions. This paper discusses the practical performance of several new algorithms designed to satisfy these conditions.

Suggested Citation

  • M. Al-Baali, 1998. "Numerical Experience with a Class of Self-Scaling Quasi-Newton Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 533-553, March.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:3:d:10.1023_a:1022608410710
    DOI: 10.1023/A:1022608410710
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    References listed on IDEAS

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    1. Shmuel S. Oren & David G. Luenberger, 1974. "Self-Scaling Variable Metric (SSVM) Algorithms," Management Science, INFORMS, vol. 20(5), pages 845-862, January.
    2. Shmuel S. Oren, 1974. "Self-Scaling Variable Metric (SSVM) Algorithms," Management Science, INFORMS, vol. 20(5), pages 863-874, January.
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    Cited by:

    1. W. Y. Cheng & D. H. Li, 2010. "Spectral Scaling BFGS Method," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 305-319, August.
    2. Neculai Andrei, 2018. "A Double-Parameter Scaling Broyden–Fletcher–Goldfarb–Shanno Method Based on Minimizing the Measure Function of Byrd and Nocedal for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 191-218, July.

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