Accelerating the LSTRS Algorithm

J. Lampe, Marielba de la Caridad Rojas Larrazabal, D.C. Sorensen, H. Voss

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    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.
    Original languageEnglish
    Place of PublicationKgs. Lyngby
    PublisherTechnical University of Denmark, DTU Informatics, Building 321
    Publication statusPublished - 2009
    SeriesIMM-Technical Report-2009-09

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