Regularization and Preconditioning of KKT Systems
Arising in Nonnegative Least-Squares Problems

Technical Report MS 2007-004

S. Bellavia, J. Gondzio and B. Morini

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 effectivness of the preconditioner and fast convergence of the iterative method established by the analysis performed in this paper.

Key words: Nonnegative Least Squares, Interior Point Methods,
Regularization, Preconditioned Indefinite System.

PDF MS07-004.pdf.

Written: August 30, 2007, revised April 15, 2008.
Numerical Linear Algebra with Applications 16 (2009) pp. 39-61.