title: On the chaotic behavior of the primal-dual affine-scaling algorithm for linear optimization.
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.
authors.affiliation: Faculty of Mathematics, University of Vienna, Oskar Morgensternplatz 1 A-1090 Vienna, Austria.
authors.forename: H
authors.initials: H
authors.lastname: Bruin
authors.affiliation: Delft University, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, Netherlands.
authors.forename: R
authors.initials: R
authors.lastname: Fokkink
authors.affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, China.
authors.forename: G
authors.initials: G
authors.lastname: Gu
authors.affiliation: Delft University, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, Netherlands.
authors.forename: C
authors.initials: C
authors.lastname: Roos