# Complexity and performance of an Augmented Lagrangian algorithm

arXiv: https://arxiv.org/abs/1907.02401 · HTML: https://mlsanity.com/paper/1907.02401/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [A first-order augmented Lagrangian method for constrained minimax optimization](https://mlsanity.com/paper/2301.02060/) (2023)
- [A Newton-CG based augmented Lagrangian method for finding a second-order stationary point of nonconvex equality constrained optimization with complexity guarantees](https://mlsanity.com/paper/2301.03139/) (2023)
- [Federated Learning with Convex Global and Local Constraints](https://mlsanity.com/paper/2310.10117/) (2023)
- [Exact and Heuristic Algorithms for Constrained Biclustering](https://mlsanity.com/paper/2508.05493/) (2025)
- [A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints](https://mlsanity.com/paper/2509.02894/) (2025)
- [A first-order method for nonconvex-strongly-concave constrained minimax optimization](https://mlsanity.com/paper/2512.22909/) (2025)

## Abstract (arXiv)

Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Mart'inez and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM Journal on Optimization 18, pp. 1286-1309, 2008]. Complexity results that report its worst-case behavior in terms of iterations and evaluations of functions and derivatives that are necessary to obtain suitable stopping criteria are presented in this work. In addition, the computational performance of a new version of the method is presented, which shows that the updated software is a useful tool for solving large-scale constrained optimization problems.