# Adaptive ADMM with Spectral Penalty Parameter Selection

arXiv: https://arxiv.org/abs/1605.07246 · HTML: https://mlsanity.com/paper/1605.07246/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2016.

## Built on by (most cited first, 10 of 10)

- [DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting](https://mlsanity.com/paper/2106.09117/) (2021)
- [A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow](https://mlsanity.com/paper/2110.11991/) (2021)
- [Federated ADMM from Bayesian Duality](https://mlsanity.com/paper/2506.13150/) (2025)
- [A Simple Adaptive Unfolding Network for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2301.10208/) (2023)
- [Learning Multi-Agent Coordination via Sheaf-ADMM](https://mlsanity.com/paper/2605.31005/) (2026)
- [Joint learning of multiple Granger causal networks via non-convex regularizations: Inference of group-level brain connectivity](https://mlsanity.com/paper/2105.07196/) (2021)
- [Interpretable factorization of clinical questionnaires to identify latent factors of psychopathology](https://mlsanity.com/paper/2312.07762/) (2023)
- [Optimizing ADMM and Over-Relaxed ADMM Parameters for Linear Quadratic Problems](https://mlsanity.com/paper/2401.00657/) (2024)
- [Optimization Problem Solving Can Transition to Evolutionary Agentic Workflows](https://mlsanity.com/paper/2505.04354/) (2025)
- [Learning Over-Relaxation Policies for ADMM with Convergence Guarantees](https://mlsanity.com/paper/2604.26932/) (2026)

## Abstract (arXiv)

The alternating direction method of multipliers (ADMM) is a versatile tool for solving a wide range of constrained optimization problems, with differentiable or non-differentiable objective functions. Unfortunately, its performance is highly sensitive to a penalty parameter, which makes ADMM often unreliable and hard to automate for a non-expert user. We tackle this weakness of ADMM by proposing a method to adaptively tune the penalty parameters to achieve fast convergence. The resulting adaptive ADMM (AADMM) algorithm, inspired by the successful Barzilai-Borwein spectral method for gradient descent, yields fast convergence and relative insensitivity to the initial stepsize and problem scaling.