Lampe, J.; Rojas, M.; Sorensen, D. C.; Voss, H. Accelerating the LSTRS algorithm. (English) Zbl 1368.65096 SIAM J. Sci. Comput. 33, No. 1, 175-194 (2011). Summary: The LSTRS software for the efficient solution of the large-scale trust-region subproblem was proposed in [M. Rojas et al., ACM Trans. Math. Softw. 34, No. 2, Art. 11, 28 p. (2008; Zbl 1291.65177)]. The LSTRS method is based on recasting the problem in terms of a parameter-dependent eigenvalue problem and adjusting the parameter iteratively. The essential work at each iteration is the solution of an eigenvalue problem for the smallest eigenvalue of a bordered Hessian matrix (or two smallest eigenvalues in the potential hard case) and associated eigenvector(s). Using the nonlinear Arnoldi method to solve the eigenvalue problems makes it possible to recycle most of the information from previous iterations which can substantially accelerate LSTRS. Cited in 13 Documents MSC: 65K10 Numerical optimization and variational techniques 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 90C20 Quadratic programming Keywords:large-scale trust-region subproblem (LSTRS); constrained quadratic optimization; regularization; trust-region; ARPACK; nonlinear Arnoldi method Citations:Zbl 1291.65177 Software:HSL; LSTRS; Regularization tools; ARPACK PDFBibTeX XMLCite \textit{J. Lampe} et al., SIAM J. Sci. Comput. 33, No. 1, 175--194 (2011; Zbl 1368.65096) Full Text: DOI Link