Convergence of Augmented Lagrangian Methods for Composite Optimization Problems
Optimization and Control
2023-10-23 v2
Abstract
Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new second-order variational property, called the semi-stability of second subderivatives, and demonstrate that it is widely satisfied for numerous classes of functions, important for applications in constrained and composite optimization problems. Using the latter condition and a certain second-order sufficient condition, we are able to establish Q-linear convergence of the primal-dual sequence for an inexact version of the ALM for composite programs.
Cite
@article{arxiv.2307.15627,
title = {Convergence of Augmented Lagrangian Methods for Composite Optimization Problems},
author = {Nguyen T. V. Hang and Ebrahim Sarabi},
journal= {arXiv preprint arXiv:2307.15627},
year = {2023}
}