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IMA Journal of Numerical Analysis Advance Access originally published online on June 20, 2008
IMA Journal of Numerical Analysis 2008 28(4):827-861; doi:10.1093/imanum/drn034
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A recursive Formula-trust-region method for bound-constrained nonlinear optimization

Serge Gratton{dagger} and Mélodie Mouffe{ddagger}

Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, Avenue Gustave Coriolis, Toulouse, France

Philippe L. Toint§ and Melissa Weber-Mendonça

Department of Mathematics, University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium

{dagger} Email: gratton{at}cerfacs.fr

{ddagger} Email: melodie.mouffe{at}cerfacs.fr

§ Corresponding author. Email: philippe.toint{at}fundp.ac.be

Email: mwm{at}math.fundp.ac.be

Received on 24 April 2007. Accepted for publication 6 May 2008.


  Abstract

A recursive trust-region method is introduced for the solution of bound-cons-trained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the trust region, which is well adapted to the handling of bounds and also to the use of successive coordinate minimization as a smoothing technique. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point.

Key Words: recursive methods; multilevel problems; nonlinear optimization; convergence theory

To Michael Powell, long-time inspirator and always friend.


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