On the chaotic behavior of the Primal--Dual Affine--Scaling Algorithm for Linear Optimization

TL;DR

This paper investigates the chaotic dynamics in primal-dual affine-scaling algorithms for linear optimization, demonstrating that such chaotic behavior is common rather than exceptional, through analysis of a family of quadratic maps.

Contribution

It provides evidence that chaos in interior point methods is a generic phenomenon, extending previous isolated observations to a broader class of problems.

Findings

Chaotic behavior is prevalent in the studied family of quadratic maps.

Chaotic dynamics are not limited to specific linear optimization problems.

The results suggest chaos is a common feature in interior point methods.

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.