Nonlinear Stepsize Control, Trust Regions and Regularizations for Unconstrained Optimization

Philippe Toint(philippe.tointfundp.ac.be)

Abstract: 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.

Keywords: nonlinear optimization, unconstrained problems, global convergence

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 3: Nonlinear Optimization (Bound-constrained Optimization )

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

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Entry Submitted: 11/06/2008
Entry Accepted: 11/06/2008
Entry Last Modified: 11/06/2008

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