Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14376
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Main Title: On the Efficient Update of Rectangular LU Factorizations subject to Low Rank Modifications
Author(s): Stange, Peter
Griewank, Andreas
Bollhöfer, Matthias
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15603
http://dx.doi.org/10.14279/depositonce-14376
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: 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.
Subject(s): KKT-System
quasi-Newton
updating factorization
LU decomposition
Issue Date: 5-Jan-2006
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F05 Direct methods for linear systems and matrix inversion
65K05 Mathematical programming
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2006, 01
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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