A Second Full - Newton Step O ( n ) Infeasible Interior - Point Algorithm for Linear Optimization ∗

In [4] the second author presented a new primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best known bound for infeasible interior-point algorithms. Each iteration consists of a step that restores the feasibility for an intermediate problem (the so-called feasibility step) and a few (usual) centering steps. No more than O(n log(n/ε)) iterations are required for getting an ε-solution of the problem at hand, which coincides with the best known bound for infeasible interior-point algorithms. In this paper we use a different feasibility step and show that with a simpler analysis the same result can be obtained.