Local analysis of the feasible primal-dual interior-point method

In this paper we analyze the rate of local convergence of the Newton primal-dual interior-point method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q-quadratic when the functions associated to the binding inequality constraints are concave. In general, the q-quadratic rate is achieved provided the step in the primal variables does not become asymptotically orthogonal to any of the gradients of the binding inequality constraints.