Stefania Bellavia, Jacek Gondzio, Benedetta Morini, Regularization and preconditioning of KKT systems arising in nonnegative least-squares problems, Numerical Linear Algebra with Applications,  Volume 16 Issue 1, Pages 39 - 61

Published Online: 9 Jul 2008

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Keywords: bound-constrained linear least-squares problems • inexact Newton methods • iterative linear solvers • KKT systems • regularization • preconditioning

 

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.