Convergence of the homotopy path for a full-Newton step infeasible interior-point method

Roos [C. Roos, A full-Newton step O(n)O(n) infeasible interior-point algorithm for linear optimization. SIAM J. Optim. 16 (4) (2006) 1110–1136 (electronic)] proposed a new primal–dual infeasible interior-point method for linear optimization. This new method can be viewed as a homotopy method. In this work, we show that the homotopy path has precisely one accumulation point in the optimal set. Moreover, this accumulation point is the analytic center of a subset of the optimal set and depends on the starting point of the infeasible interior-point method.