An Improved and Simplified Full-Newton Step $O(n)$ Infeasible Interior-Point Method for Linear Optimization

Abstract

We present an improved version of an infeasible interior-point method for linear optimization published in 2006. In the earlier version each iteration consisted of one so-called feasibility step and a few---at most three---centering steps. In this paper each iteration consists of only a feasibility step, whereas the iteration bound improves the earlier bound by a factor $2\sqrt{2}$. The improvements are due to a new lemma that gives a much tighter upper bound for the proximity after the feasibility step.