Superlinear convergence of infeasible-interior-point methods for linear programming

At present the interior-point methods of choice are primal-dual infeasible-interior-point methods, where the iterates are kept positive, but allowed to be infeasible. In practice, these methods have demonstrated superior computational performance. from a theoretical point of view, however, they have not been as thoroughly studied as their counterparts-feasible-interior-point methods, where the iterates are required to be strictly feasible. Recently, Kojima et al, Zhang, Mizuno and Potra studied the global convergence of algorithms in the primal-dual infeasible-interior-point framework. In this paper, the authors continue to study this framework, and in particular they study the local convergence properties of algorithms in this framework. The authors construct parameter selections that lead to Q-superlinear convergence for a merit function and R-superlinear convergence for the iteration sequence, both at rate 1+τ where τ can be arbitrarily close to one.