An interior point method for linear programming based on a class of kernel functions

Interior point methods are not only the most effective methods for solving optimisation problems in practice but they also have polynomial time complexity. However, there is still a gap between the practical behavior of the interior point method algorithms and their theoretical complexity results. In this paper, by focusing on linear programming problems, we introduce a new family of kernel functions that have some simple and easy to check properties. We present a simplified analysis to obtain the complexity of generic interior point methods based on the proximity functions induced by these kernel functions. Finally, we prove that this family of kernel functions leads to improved iteration bounds of the large-update interior point methods.