# Complexity and performance of an Augmented Lagrangian algorithm

## TL;DR

This paper analyzes the complexity and worst-case performance of the Algencan augmented Lagrangian algorithm and demonstrates its effectiveness for large-scale constrained optimization problems.

## Contribution

It provides new complexity results for Algencan and evaluates a new software version showing improved computational performance.

## Key findings

- Complexity bounds for Algencan's iteration and evaluation counts.
- Empirical evidence of the new version's efficiency on large-scale problems.
- Algencan's robustness and practicality in constrained optimization.

## Abstract

Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Mart\'{\i}nez 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.