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A Retrospective Trust-Region Method for Unconstrained Optimization

Fabian Bastin (bastin***at***iro.umontreal.ca)
Vincent Malmedy (vincent.malmedy***at***fundp.ac.be)
Mélodie Mouffe (melodie.mouffe***at***cerfacs.fr)
Philippe L. Toint (philippe.toint***at***fundp.ac.be)
Dimitri Tomanos (dimitri.tomanos***at***fundp.ac.be)

Abstract: We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to first- and second-order critical points is proved under classical assumptions and preliminary numerical experiments on CUTEr problems indicate that the new method is very competitive.

Keywords: unconstrained minimization, trust-region methods, convergence theory, numerical experiments

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Report 07/08, Department of Mathematics, FUNDP-University of Namur, Namur, Belgium

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Entry Submitted: 10/31/2007
Entry Accepted: 10/31/2007
Entry Last Modified: 11/05/2007

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