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

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 √ 2. The improvements are due to a new lemma that gives a much tighter upper bound for the proximity after the feasibility step.