TY - GEN A1 - Stange, Peter A1 - Griewank, Andreas A1 - Bollhöfer, Matthias T1 - On the Efficient Update of Rectangular LU Factorizations subject to Low Rank Modifications N2 - 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. KW - KKT-System KW - quasi-Newton KW - updating factorization KW - LU decomposition Y1 - 2006 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/316 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3165 ER -