Algorithm 873: LSTRS: MATLAB Software for Large-Scale Trust-Region Subproblems and Regularization

A MATLAB 6.0 implementation of the LSTRS method is resented. LSTRS was described in Rojas, M., Santos, S.A., and Sorensen, D.C., 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 matrix-vector multiplication routine. Therefore, the implementation preserves the matrix-free nature of the method. A description of the LSTRS method and of the MATLAB software, version 1.2, is presented. Comparisons with other techniques and applications of the method are also included. A guide for using the software and examples are provided.