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Abstract
A class of algorithms for unconstrained optimization is introduced, which subsumes the classical trust-region algorithm and two of its newer variants, as well as the cubic and quadratic regularization methods. A unified theory of global convergence to first-order critical points is then described for this class.
Acknowledgements
The author is indebted to B. Morini, D. Tomanos and M. Porcelli for their suggestions on this paper and to two anonymous referees whose comments on a first draft of this paper led to the present (tardy) revision.
Notes
The update described here is that proposed in Citation25. Fan Citation12 used a very similar update, which is closer to that of Citation15.
When considering Cauchy decrease only.