Artículos de revistas
A new matrix-free algorithm for the large-scale trust-region subproblem
Registro en:
Siam Journal On Optimization. Siam Publications, v. 11, n. 3, n. 611, n. 646, 2001.
1052-6234
WOS:000167675100003
10.1137/S105262349928887X
Autor
Rojas, M
Santos, SA
Sorensen, DC
Institución
Resumen
We present a new method for the large-scale trust-region subproblem. The method is matrix-free in the sense that only matrix-vector products are required. We recast the trust-region subproblem as a parameterized eigenvalue problem and compute an optimal value for the parameter. We then nd the solution of the trust-region subproblem from the eigenvectors associated with two of the smallest eigenvalues of the parameterized eigenvalue problem corresponding to the optimal parameter. The new algorithm uses a different interpolating scheme than existing methods and introduces a uni ed iteration that naturally includes the so-called hard case. We show that the new iteration is well defined and convergent at a superlinear rate. We present computational results to illustrate convergence properties and robustness of the method. 11 3 611 646