On the chaotic behavior of the primal-dual affine-scaling algorithm for linear optimization

H Bruin; R Fokkink; G Gu; C Roos

doi:10.1063/1.4902900

On the chaotic behavior of the primal-dual affine-scaling algorithm for linear optimization

Chaos. 2014 Dec;24(4):043132. doi: 10.1063/1.4902900.

Authors

H Bruin¹, R Fokkink², G Gu³, C Roos²

Affiliations

¹ Faculty of Mathematics, University of Vienna, Oskar Morgensternplatz 1 A-1090 Vienna, Austria.
² Delft University, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, Netherlands.
³ Department of Mathematics, Nanjing University, Nanjing 210093, China.

PMID: 25554052
DOI: 10.1063/1.4902900

Abstract

We study a one-parameter family of quadratic maps, which serves as a template for interior point methods. It is known that such methods can exhibit chaotic behavior, but this has been verified only for particular linear optimization problems. Our results indicate that this chaotic behavior is generic.