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.
Technical Report MS-07-004, School of Mathematics, The University of Edinburgh, August 31, 2007.