An inexact Newton method combined with Hestenes multipliers' scheme for the solution of Karush-Kuhn-Tucker systems

In this work a Newton interior–point method for the solution of Karush– Kuhn–Tucker systems is presented. A crucial feature of this iterative method is the solution, at each iteration, of the inner subproblem. This subproblem is a linear–quadratic programming problem, that can solved approximately by an inner iterative method such as the Hestenes multipliers’ method. A deep analysis on the choices of the parameters of the method (perturbation and damping parameters) has been done. The global convergence of the Newton interior–point method is proved when it is viewed as an inexact Newton method for the solution of nonlinear systems with restriction on the sign of some variables. The Newton interior–point method is numerically evaluated on large scale test problems arising from elliptic optimal control problems which show the effectiveness of the approach.