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

Paul Armand (1) , Joël Benoist (2) , Riadh Omheni (2)

1 XLIM - XLIM
2 XLIM-DMI - DMI

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.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Paul Armand, Joël Benoist, Riadh Omheni. A primal-dual augmented Lagrangian method for non-linear optimization. EUROPT 2013, Jun 2013, Florence, Italy. ⟨hal-00920243⟩