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Approximating Jacobians by the TR2 formula
Author(s) -
Griewank Andreas,
Korzec Maciek
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510370
Subject(s) - jacobian matrix and determinant , karush–kuhn–tucker conditions , rank (graph theory) , context (archaeology) , computer science , nonlinear system , mathematical optimization , mathematics , algebra over a field , pure mathematics , combinatorics , physics , paleontology , quantum mechanics , biology
Abstract In the context of KKT systems for nonlinear optimization one wishes to approximate rectangular Jacobian matrices of active constraints. A possible approximation is the Two‐Sided‐Rank‐One update (TR1) motivated in [1]. Since its denominator can easily become small we tried to prevent a possible blow up and achieve better approximations with the newly introduced Two‐Sided‐Rank‐Two update (TR2), which otherwise preserves the good qualities of the TR1. We motivate, introduce and discuss the two low‐rank‐updates. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)