Sorensen, D. C. Minimization of a large-scale quadratic function subject to a spherical constraint. (English) Zbl 0878.65044 SIAM J. Optim. 7, No. 1, 141-161 (1997). An algorithm for solving the large scale trust-region subproblem is proposed that requires a fixed-size limited storage proportional to the order of the quadratic function and relies only upon matrix-vector products. It recasts the problem in terms of a parameterized eigenvalue problem, but only the smallest eigenvalue and corresponding eigenvector needs to be computed using the implicitly restarted Lanczos method. Reviewer: P.Pan (Nanjing) Cited in 37 Documents MSC: 65K05 Numerical mathematical programming methods 90C06 Large-scale problems in mathematical programming 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 90C20 Quadratic programming Keywords:large scale quadratic function; spherical constraint; algorithm; large scale trust-region subproblem; parameterized eigenvalue problem; eigenvector; implicitly restarted Lanczos method PDFBibTeX XMLCite \textit{D. C. Sorensen}, SIAM J. Optim. 7, No. 1, 141--161 (1997; Zbl 0878.65044) Full Text: DOI