# Adaptive inexact fast augmented Lagrangian methods for constrained convex optimization

arXiv: https://arxiv.org/abs/1505.03175 · HTML: https://mlsanity.com/paper/1505.03175/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2015.

## Built on by (most cited first, 5 of 5)

- [Accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient](https://mlsanity.com/paper/2206.01209/) (2022)
- [Federated Learning with Convex Global and Local Constraints](https://mlsanity.com/paper/2310.10117/) (2023)
- [Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraints](https://mlsanity.com/paper/2311.09065/) (2023)
- [A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints](https://mlsanity.com/paper/2509.02894/) (2025)
- [Global Optimality for Constrained Exploration via Penalty Regularization](https://mlsanity.com/paper/2604.28144/) (2026)

## Abstract (arXiv)

In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in [15] and the newly introduced inexact oracle framework from [4]. We analyze several algorithmic instances with constant and adaptive smoothing parameters and derive total computational complexity results in terms of projections onto a simple primal set. For the basic inexact fast augmented Lagrangian algorithm we obtain the overall computational complexity of order Oleft(frac1ε5/4right), while for the adaptive variant we get Oleft(frac1εright), projections onto a primal set in order to obtain an ε-optimal solution for our original problem.