A MIXED LOGARITHMIC BARRIER-AUGMENTED LAGRANGIAN ALGORITHM FOR CONSTRAINED OPTIMIZATION

Paul Armand (1) , Riadh Omheni (1)

1 XLIM-DMI - DMI

We present a primal-dual algorithm for solving a constrained optimization problem. The method is based on a Newtonian method applied to a sequence of perturbed KKT systems. These systems follow from a reformulation of the initial problem under the form of a sequence of penalized problems, by introducing an augmented Lagrangian for handling the equality constraints and a log-barrier penalty for the inequalities. We detail the updating rules for monitoring the different parameters (Lagrange multiplier estimates, quadratic penalty parameter and log-barrier parameter), in order to get strong global convergence properties and an asymptotic q-superlinear rate of convergence. We show also that the advantage of this approach is that it introduces a natural regularization of the linear system to solve at each iteration, when solving a degenerate problem for which the Jacobian of constraints is rank deficient.

Mots clés: Nonlinear optimization; Interior point methods; Augmented Lagrangian; Logarithmic barrier

Domaines: Optimisation et contrôle [math.OC]

Paul Armand, Riadh Omheni. A MIXED LOGARITHMIC BARRIER-AUGMENTED LAGRANGIAN ALGORITHM FOR CONSTRAINED OPTIMIZATION. ALEL 2014, IMUS, Universidad de Sevilla, Jun 2014, Séville, Spain. ⟨hal-01316930⟩