Title: What is wrong with the logarithmic barrier function?

Interior-point methods (IPMs) for Linear Optimization can use small or large updates of the barrier parameter. Contrary to theoretical results, large-update IPMs are more efficient in practice than small-update IPMs. Recently this gap between theory and practice has been narrowed by introducing new barrier functions. In this talk we discuss the theoretical weaknesses of the classical approach to large-update methods and we show how better complexity results can be obtained by changing the barrier function. The behavior of several barrier functions will be reviewed. We also provide new evidence that the worst case behavior of the classical logarithmic barrier method is the reason for the aforementioned gap.