|
|||||
|
|
Regularization and preconditioning of KKT systems arising in nonnegative least‐squares problems |
|
| Authors: | Stefania Bellavia Jacek Gondzio Benedetta Morini |
| Institution: | 1. Dipartimento di Energetica ‘S. Stecco’, Università di Firenze, via C. Lombroso 6/17, 50134 Firenze, Italy;2. School of Mathematics, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland, U.K. |
| Abstract: | A regularized Newton‐like method for solving nonnegative least‐squares problems is proposed and analysed in this paper. A preconditioner for KKT systems arising in the method is introduced and spectral properties of the preconditioned matrix are analysed. A bound on the condition number of the preconditioned matrix is provided. The bound does not depend on the interior‐point scaling matrix. Preliminary computational results confirm the effectiveness of the preconditioner and fast convergence of the iterative method established by the analysis performed in this paper. Copyright © 2008 John Wiley & Sons, Ltd. |
| Keywords: | bound‐constrained linear least‐squares problems inexact Newton methods iterative linear solvers KKT systems regularization preconditioning |