A recursive \(\ell_{\infty}\)-trust-region method for bound-constrained nonlinear optimization. (English) Zbl 1156.65060

Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L.; Weber-Mendonça, Melissa

IMA J. Numer. Anal. 28, No. 4, 827-861 (2008).

Authors’ summary: 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. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point.

Reviewer: Klaus Schittkowski (Bayreuth)

MSC:

65K05	Numerical mathematical programming methods
90C30	Nonlinear programming
90C06	Large-scale problems in mathematical programming
90C51	Interior-point methods

Keywords:

recursive methods; multilevel problems; convergence; numerical examples; bound constraints; large scale optimization; trust-region methods; infinite dimensional problems; nonlinear nonconvex optimization