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Numerical Experience with a Recursive Trust-Region Method for Multilevel Nonlinear Optimization

Serge Gratton (serge.gratton***at***cerfacs.fr)
Annick Sartenaer (annick.sartenaer***at***fundp.ac.be)
Philippe L. Toint (philippe.toint***at***fundp.ac.be)

Abstract: We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer, Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm's parameters is identified on these problems, yielding a very satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared to alternative optimization techniques such as mesh refinement and direct solution of the fine-level problem. The sensibility of the default variant with respect to most important algorithmic parameters is finally investigated.

Keywords: nonlinear optimization, multilevel problems, simplified models, recursive algorithms, numerical performance

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Technical Report 06/01, Department of Mathematics, University of Namur, Namur, Belgium, 2006.

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Entry Submitted: 06/23/2006
Entry Accepted: 06/23/2006
Entry Last Modified: 06/23/2006

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