A MIXED LOGARITHMIC BARRIER-AUGMENTED LAGRANGIAN ALGORITHM FOR CONSTRAINED OPTIMIZATION

International audienceWe present a primal-dual algorithm for solving a constrained optimizationproblem. The method is based on a Newtonian method applied to a sequence ofperturbed KKT systems. These systems follow from a reformulation of the initialproblem under the form of a sequence of penalized problems, by introducing anaugmented Lagrangian for handling the equality constraints and a log-barrierpenalty for the inequalities. We detail the updating rules for monitoring thedifferent parameters (Lagrange multiplier estimates, quadratic penalty parameterand log-barrier parameter), in order to get strong global convergence propertiesand an asymptotic q-superlinear rate of convergence. We show also that theadvantage of this approach is that it introduces a natural regularization of thelinear system to solve at each iteration, when solving a degenerate problem forwhich the Jacobian of constraints is rank deficient