# Local Convergence Analysis of Augmented Lagrangian Methods for Piecewise Linear-Quadratic Composite Optimization Problems

arXiv: https://arxiv.org/abs/2010.11379 · HTML: https://mlsanity.com/paper/2010.11379/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## 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)

Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear convergence of the primal-dual sequence, generated by the augmented Lagrangian method for piecewise linear-quadratic composite optimization problems, even when the Lagrange multiplier in this class of problems is not unique. Furthermore, we establish the equivalence between the second-order sufficient condition and the quadratic growth condition of the augmented Lagrangian problem for this class of composite optimization problems.