LSTRS Software Manual

The software manual of a MATLAB 6.0 implementation of the LSTRS method is presented. LSTRS was described in M. Rojas, S.A. Santos and D.C. Sorensen, A new matrix-free method for the large-scale trust-region subproblem, SIAM J. Optim., 11(3):611-646, 2000. LSTRS is designed for large-scale quadratic problems with one norm constraint. The method is based on a reformulation of the trust-region subproblem as a parameterized eigenvalue problem, and consists of an iterative procedure that finds the optimal value for the parameter. The adjustment of the parameter requires the solution of a large-scale eigenvalue problem at each step. LSTRS relies on matrix-vector products only and has low and fixed storage requirements, features that make it suitable for large-scale computations. In the MATLAB implementation, the Hessian matrix of the quadratic objective function can be specified either explicitly, or in the form of a matrixvector multiplication routine. Therefore, the implementation preserves the matrix-free nature of the method. A description of the MATLAB software, version 1.2, is presented. A guide for using the software and examples are provided.