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Tyings in linear systems of equations modelled with positive and negative penalty functions

✍ Scribed by Askes, Harm ;Piercy, Stewart ;Ilanko, Sinniah

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 81 KB
Volume: 24
Category: Article
ISSN: 1069-8299
DOI: 10.1002/cnm.1023

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✦ Synopsis

Abstract

In this short note, we focus on tyings (constraints that relate multiple degrees of freedom) modelled by means of penalty functions. In contrast to what is commonly thought, it is possible to obtain convergent results when negative penalty parameters are taken. A mathematical proof and an illustrating example are provided. In particular, we have proven that the results obtained with positive and negative penalty parameters enclose the exact solution from opposite sides. To this end, we have investigated a pseudo‐force that is defined as the derivative of the constraint with respect to the inverse penalty parameter. Copyright © 2007 John Wiley & Sons, Ltd.

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