The aim of this talk is to render the power of (short-step) interior-point methods for linear programming (and by extension, convex programming) intuitively understandable to those who have a basic training in numerical methods for dynamical systems solving. The connection between the two areas is made by interpreting line-search methods in a forward Euler framework, and by analysing the algorithmic complexity in terms of the stiffness of the vector field of search directions. Our analysis cannot replicate the best complexity bounds, but due to its weak assumptions it also applies to inexactly computed search directions and has explanatory power for a wide class of algorithms.
Co-Author: Coralia Cartis, Edinburgh University School of Mathematics.