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

Stefania Bellavia(stefania.bellavia***at***unifi.it)
Jacek Gondzio(J.Gondzio***at***ed.ac.uk)
Benedetta Morini(benedetta.morini***at***unifi.it)

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.

Keywords: regularization, preconditioning, KKT systems, Interior Point methods, nonnegative least-squares problems

Category 1: Nonlinear Optimization (Bound-constrained Optimization )

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

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Entry Submitted: 09/01/2007
Entry Accepted: 09/01/2007
Entry Last Modified: 09/01/2007

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