# Convergence of Augmented Lagrangian Methods for Composite Optimization Problems

arXiv: https://arxiv.org/abs/2307.15627 · HTML: https://mlsanity.com/paper/2307.15627/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [Nonmonotone subgradient methods based on a local descent lemma](https://mlsanity.com/paper/2510.19341/) (2025)

## Abstract (arXiv)

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.