A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization

作者：Armand Paul^*; Omheni Riadh

来源：Journal of Optimization Theory and Applications, 2017, 173(2): 523-547.

DOI：10.1007/s10957-017-1071-x

• Nonlinear optimization
• Constrained optimization
• Augmented Lagrangian
• Primal-dual methods
• Interior-point methods

We present a primal-dual algorithm for solving a constrained optimization problem. This 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 estimate, quadratic penalty and log-barrier parameter), in order to get strong global convergence properties. We show that one advantage of this approach is that it introduces a natural regularization of the linear system to solve at each iteration, for the solution of a problem with a rank deficient Jacobian of constraints. The numerical experiments show the good practical performances of the proposed method especially for degenerate problems.

• 出版日期2017-5