Nonlinear Stepsize Control, Trust Regions and Regularizations for Unconstrained Optimization

A general 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. An extension to projection-based trust-region algorithms for nonlinear optimization over convex sets is also presented.

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Report TR08-15, Department of Mathematics, FUNDP-University of Namur, Namur, Belgium

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