A globally and quadratically convergent primal-dual augmented Lagrangian algorithm for equality constrained minimization

par Omheni Riadh (XLIM-DMI Limoges)

vendredi 16 mai 2014, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

We propose a new primal-dual augmented Lagrangian method for solving equality constrained minimization problems. This algorithm is based on a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing an augmented Lagrangian to handle equality constraints. An important aspect of this new approach is that the algorithm reduces asymptotically to a regularized Newton method applied to KKT conditions of the original problem. The global convergence and the asymptotic properties of the algorithm are presented. In particular, a quadratic convergence rate is obtained by carefully controlling the parameters. Some numerical results, showing the efficiency and robustness of the proposed method, are reported.