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On the Efficient Update of Rectangular LU Factorizations subject to Low Rank Modifications

Please always quote using this URN:urn:nbn:de:0296-matheon-3165
  • In this paper we introduce a new method for the computation of KKT matrices that arise from solving constrained, nonlinear optimization problems. This method requires updating of null-space factorizations after a low rank modification. The update procedure has the advantage that it is significantly cheaper than a re-factorization of the system at each new iterate. This paper focuses on the cheap update of a rectangular LU decomposition after a rank-1 modification. Two different procedures for updating the LU factorization are presented in detail and compared regarding their costs of computation and their stability. Moreover we will introduce an extension of these algorithms which further improves the computation time. This turns out to be an excellent alternative to algorithms based on orthogonal transformations.

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Metadaten
Author:Peter Stange, Andreas Griewank, Matthias Bollhöfer
URN:urn:nbn:de:0296-matheon-3165
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/09/01
Release Date:2006/09/01
Tag:
Institute:Humboldt-Universität zu Berlin
Technische Universität Berlin
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F05 Direct methods for linear systems and matrix inversion
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K05 Mathematical programming methods [See also 90Cxx]
Preprint Number:304
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