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A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization

Serge Gratton (gratton***at***cerfacs.fr)
Mélodie Mouffe (melodie.mouffe***at***cerfacs.fr)
Philippe Toint (philippe.toint***at***fundp.ac.be)
Melissa Weber-Mendonca (mwm***at***math.fundp.ac.be)

Abstract: A recursive trust-region method is introduced for the solution of bound-constrained 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. Some numerical tests are presented to motivate a theoretical analysis showing convergence to first-order critical points irrespective of the given starting point.

Keywords: Recursive methods, multilevel problems, nonlinear optimization, convergence theory

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Bound-constrained Optimization )

Category 3: Nonlinear Optimization (Unconstrained Optimization )

Citation: IMAJNA, vol. 8(4), pages = {827-861}, year = 2008

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Entry Submitted: 04/24/2007
Entry Accepted: 04/24/2007
Entry Last Modified: 02/20/2009

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