Adaptive Augmented Lagrangian Methods for Large-Scale Equality Constrained Optimization

We propose an augmented Lagrangian algorithm for solving large-scale equality constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the core augmented Lagrangian framework, such as its attractive local convergence behavior and ability to be implemented matrix-free. This latter strength is particularly important due to interests in employing augmented Lagrangian algorithms for solving large-scale optimization problems. We focus on a trust region algorithm, but also propose a line search algorithm that employs the same adaptive penalty parameter updating scheme. We provide theoretical results related to the global convergence behavior of our algorithms and illustrate by a set of numerical experiments that they outperform traditional augmented Lagrangian methods in terms of critical performance measures.