Print Email Facebook Twitter Computational and sensitivity aspects of eigenvalue-based methods for the large-scale trust-region subproblem Title Computational and sensitivity aspects of eigenvalue-based methods for the large-scale trust-region subproblem Author Rojas, M. Fotland, B.H. Steihaug, T. Faculty Electrical Engineering, Mathematics and Computer Science Date 2011-12-31 Abstract The trust-region subproblem of minimizing a quadratic function subject to a norm constraint arises in the context of trust-region methods in optimization and in the regularization of discrete forms of ill-posed problems, including non-negative regularization by means of interior-point methods. A class of efficient methods and software for solving large-scale trust-region subproblems is based on a parametric-eigenvalue formulation of the subproblem. The solution of a sequence of large symmetric eigenvalue problems is the main computation in these methods. In this work, we study the robustness and performance of eigenvalue-based methods for the large-scale trust-region subproblem. We describe the eigenvalue problems and their features, and discuss the computational challenges they pose as well as some approaches to handle them. We present results from a numerical study of the sensitivity of solutions to the trust-region subproblem to eigenproblem solutions. To reference this document use: http://resolver.tudelft.nl/uuid:a59bcd3c-0635-4a3a-923c-1a543ba6f923 Publisher Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematical Analysis ISSN 1389-6520 Source Reports of the Department of Applied Mathematical Analysis, 11-09 Part of collection Institutional Repository Document type report Rights (c)2011 Rojas, M., Fotland, B.H., Steihaug, T. Files PDF Marielba_11-09.pdf 300.54 KB Close viewer /islandora/object/uuid:a59bcd3c-0635-4a3a-923c-1a543ba6f923/datastream/OBJ/view