A primal-dual augmented Lagrangian method for non-linear optimization

Abstract : We present a primal-dual augmented Lagrangian algorithm for NLP. The algorithm is based on the Newton method applied to a sequence of per- turbed KKT systems which comes by introducing both an augmented La- grangian and a log-barrier penalty. The globalization is done by means of a control of the iterates in the primal-dual space all along the iterations. Global and asymptotic convergence results are shown. Numerical tests are also presented. We show that the method is robust in the sense that it is able to solve degenerate problems for which the Jacobian of constraints is rank deficient.