Coleman, Thomas F.; Li, Yuying A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables. (English) Zbl 0861.65053 SIAM J. Optim. 6, No. 4, 1040-1058 (1996). The authors propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indefinite) quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem. This new method exhibits strong convergence properties and global and second-order convergence and appears to have significant practical potential. Strictly feasible points are generated. The experimental results on moderately large and sparse problems based on both sparse Cholesky and preconditioned conjugate gradient linear solvers are presented. Reviewer: N.Djuranović-Miličić (Beograd) Cited in 46 Documents MSC: 65K05 Numerical mathematical programming methods 90C20 Quadratic programming 90C06 Large-scale problems in mathematical programming Keywords:interior Newton method; interior point method; quadratic programming; sparse Cholesky method; preconditioned conjugate gradient method; reflective Newton method; large-scale problem; convergence Software:GQTPAR PDFBibTeX XMLCite \textit{T. F. Coleman} and \textit{Y. Li}, SIAM J. Optim. 6, No. 4, 1040--1058 (1996; Zbl 0861.65053) Full Text: DOI