Kahan's KGD step-size is shown to converge at least R-linearly with rate 1-1/cond(H) for quadratics, and an adaptive generalization for general optimization is proved and tested.
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Kahan's Automatic Step-Size Control for Unconstrained Optimization
Kahan's KGD step-size is shown to converge at least R-linearly with rate 1-1/cond(H) for quadratics, and an adaptive generalization for general optimization is proved and tested.