Analysis of the convergence of an inexact Newton method for solving Karush-Kuhn-Tucker systems

In this paper we analyze an interior point method for solving perturbed Karush-Kuhn-Tucker systems in the framework of inexact Newton methods. This gives the possibility to revise the method to introduce an adaptive technique for changing the perturbation parameter and an inner linear solver for determining an approximate solution of the perturbed Newton equation. It makes the method more robust and highly effective for large-scale optimization problems, as those that occur in data fitting applications and in the discretization of optimal control problems governed by partial differential equations.