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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, UAE University, Al-Ain, United Ara

    M. Al-Baali (Head)

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  1. M. Al-Baali
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Al-Baali, M. Numerical Experience with a Class of Self-Scaling Quasi-Newton Algorithms. Journal of Optimization Theory and Applications 96, 533–553 (1998). https://doi.org/10.1023/A:1022608410710

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