A perturbed-damped Newton method for large-scale constrained optimization

In this work we analyze the Newton interior-point method presented in [El-Bakry, Tapia et al., J.Optim. Theory Appl., 89, 1996] for solving constrained systems of nonlinear equations arising from the Karush-Kuhn-Tucker conditions for nonlinear programming problems (KKT systems). More specifically, we consider a variant of the Newton interior-point method for KKT systems in in which the possibility to adaptively modify the perturbation parameter and the accuracy of the solution of the perturbed Newton equation, when one is still far away from the solution at an early stage, will moderate the difficulty of solving the KKT system. Using the results in [Durazzi, J.Optim. Theory Appl., 104, 2000] and [Bellavia, J.Optim. Theory Appl., 96, 1998], it is possible to establish a global convergence theory for this modified method. The method proposed in this work can be used effectively for large-scale optimization problems with structured sparsity, which occur, for instance, from the discretization of optimal control problems with inequality constraints.