Bellavia, Stefania; Morini, Benedetta Subspace trust-region methods for large bound-constrained nonlinear equations. (English) Zbl 1128.65033 SIAM J. Numer. Anal. 44, No. 4, 1535-1555 (2006). Authors’ abstract: Trust-region methods for solving large bound-constrained nonlinear systems are considered. These allow for spherical or elliptical trust regions where the search for an approximate solution is restricted to a low-dimensional space. A general formulation for these methods is introduced and global and superlinear/quadratic convergence is shown under standard assumptions. Viable approaches for implementation in conjunction with Krylov methods are discussed and the practical performance of the resulting algorithms is shown. Reviewer: B. Döring (Düsseldorf) Cited in 24 Documents MSC: 65H10 Numerical computation of solutions to systems of equations 90C06 Large-scale problems in mathematical programming Keywords:bound-constrained nonlinear systems; subspace trust-region methods; inexact Newton step; Krylov subspace methods; superlinear/quadratic convergence; algorithms Software:NITSOL; GQTPAR; KELLEY PDFBibTeX XMLCite \textit{S. Bellavia} and \textit{B. Morini}, SIAM J. Numer. Anal. 44, No. 4, 1535--1555 (2006; Zbl 1128.65033) Full Text: DOI