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ABSTRACT An upper bound for condition number of the scaled memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) updating formula in the matrix norm is given. Then, in order to increase numerical stability of the… Click to show full abstract
ABSTRACT An upper bound for condition number of the scaled memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) updating formula in the matrix norm is given. Then, in order to increase numerical stability of the related method, the suggested bound is minimized as well and consequently, a class of choices for the scaling parameter is achieved, including the Oren–Spedicato formula as an especial case and guaranteeing the descent property. An approximate value for the most effective member of the suggested class is proposed based on the numerical observations.
Journal Title: International Journal of Computer Mathematics
Year Published: 2019
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