Accelerating the LSTRS Algorithm

In a recent paper [Rojas, Santos, Sorensen: ACM ToMS 34 (2008), Article 11] an efficient method for solving the Large-Scale Trust-Region Subproblem was suggested which is based on recasting it 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 the Hessian matrix (or two smallest eigenvalues in the potential hard case) and associated eigenvector(s). Replacing the implicitly restarted Lanczos method in the original paper with the Nonlinear Arnoldi method makes it possible to recycle most of the work from previous iterations which can substantially accelerate LSTRS. Key words. constrained quadratic optimization, regularization, trust-region, ARPACK, Nonlinear Arnoldi method AMS subject classification. 65F15, 65F22, 65F30

• Type: Journal
• Year: 2011
• Where: SIAMSC
• Authors: Jörg Lampe, Marielba Rojas, Danny C. Sorensen, Heinrich Voss
• Keywords: Eigenvalue Problem, Nonlinear Arnoldi, SIAMSC 2011, Smallest Eigenvalues