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

Serge Gratton, M. Mouffe, Philippe Toint, M. Weber-Mendona

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)827-861
Number of pages35
JournalIMA Journal of Numerical Analysis
Volume28
Issue number4
DOIs
Publication statusPublished - 1 Oct 2008

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Trust Region Method
Recursive Method
Constrained Optimization
Nonlinear Optimization
Trust Region
Smoothing Techniques
Nonconvex Optimization
Nonconvex Problems
Critical point
Theoretical Analysis
Discretization
Infinity
Optimization Problem
First-order
Norm
Hierarchy

Cite this

Gratton, Serge ; Mouffe, M. ; Toint, Philippe ; Weber-Mendona, M. / A recursive ℓ-trust-region method for bound-constrained nonlinear optimization. In: IMA Journal of Numerical Analysis. 2008 ; Vol. 28, No. 4. pp. 827-861.
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A recursive ℓ-trust-region method for bound-constrained nonlinear optimization. / Gratton, Serge; Mouffe, M.; Toint, Philippe; Weber-Mendona, M.

In: IMA Journal of Numerical Analysis, Vol. 28, No. 4, 01.10.2008, p. 827-861.

Research output: Contribution to journalArticle

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