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séminaires : "An augmented Lagrangian method for equality constrained optimization with fast infeasibility detection " - MATHIS -

We present a primal-dual augmented Lagrangian method for solving  an equality constrained minimization problem. The method is based on a  modification of the SPDOPT-AL algorithm [1,2]. Our objective is  to help the  algorithm to detect  infeasibility more rapidly. In particular, a new parameter is introduced to scale the objective function and, in case of infeasibility, to force the  convergence of the iterates to an infeasible stationary point. We show that when the algorithm converges to an infeasible stationary point, the rate of convergence is quadratic. This result is new  for the class of augmented Lagrangian methods. Finally, we compare our approach to SPDOPT-AL to show the good performance of the new algorithm.

[1] Paul Armand and Riadh Omheni. A globally and quadratically convergent primal-dual augmented Lagrangian algorithm for equality constrained optimization. Optimization Methods and Software. 2017.

[2] Paul Armand and Riadh Omheni. A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization. Journal of Optimization Theory and Applications. 2017