# An Accelerated Inexact Dampened Augmented Lagrangian Method for Linearly-Constrained Nonconvex Composite Optimization Problems

arXiv: https://arxiv.org/abs/2110.11151 · HTML: https://mlsanity.com/paper/2110.11151/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2021.

## Built on by (most cited first, 3 of 3)

- [Oracle Complexity of Single-Loop Switching Subgradient Methods for Non-Smooth Weakly Convex Functional Constrained Optimization](https://mlsanity.com/paper/2301.13314/) (2023)
- [Stochastic Smoothed Primal-Dual Algorithms for Nonconvex Optimization with Linear Inequality Constraints](https://mlsanity.com/paper/2504.07607/) (2025)
- [Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraints](https://mlsanity.com/paper/2311.09065/) (2023)

## Abstract (arXiv)

This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL method consists of: (i) inexactly solving a dampened proximal augmented Lagrangian (AL) subproblem by calling an accelerated composite gradient (ACG) subroutine; (ii) applying a dampened and under-relaxed Lagrange multiplier update; and (iii) using a novel test to check whether the penalty parameter of the AL function should be increased. Under several mild assumptions involving the dampening factor and the under-relaxation constant, it is shown that the AIDAL method generates an approximate stationary point of the constrained problem in cal O(varepsilon-5/2logvarepsilon-1) iterations of the ACG subroutine, for a given tolerance varepsilon>0. Numerical experiments are also given to show the computational efficiency of the proposed method.