# Differentiable Linearized ADMM

arXiv: https://arxiv.org/abs/1905.06179 · HTML: https://mlsanity.com/paper/1905.06179/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 18 of 18)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [Towards Constituting Mathematical Structures for Learning to Optimize](https://mlsanity.com/paper/2305.18577/) (2023)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Graph Denoising with Framelet Regularizer](https://mlsanity.com/paper/2111.03264/) (2021)
- [A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow](https://mlsanity.com/paper/2110.11991/) (2021)
- [Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training](https://mlsanity.com/paper/2206.07875/) (2022)
- [Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks](https://mlsanity.com/paper/2204.11640/) (2022)
- [Learning to Accelerate Approximate Methods for Solving Integer Programming via Early Fixing](https://mlsanity.com/paper/2207.02087/) (2022)
- [Hierarchical Optimization-Derived Learning](https://mlsanity.com/paper/2302.05587/) (2023)
- [Accelerating Multi-Block Constrained Optimization Through Learning to Optimize](https://mlsanity.com/paper/2409.17320/) (2024)
- [DiffCoord: Differentiable Coordination for Distributed Multi-Agent Trajectory Optimization](https://mlsanity.com/paper/2509.01630/) (2025)
- [A Design Space Study for LISTA and Beyond](https://mlsanity.com/paper/2104.04110/) (2021)
- [SymNMF-Net for The Symmetric NMF Problem](https://mlsanity.com/paper/2205.13214/) (2022)
- [Learning to Optimize by Differentiable Programming](https://mlsanity.com/paper/2601.16510/) (2026)
- [Learned Interpretable Residual Extragradient ISTA for Sparse Coding](https://mlsanity.com/paper/2106.11970/) (2021)

## Abstract (arXiv)

Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed inverse problems, but there is still a scarcity of rigorous analysis about the convergence behaviors of learning-based optimization. In particular, most existing analyses are specific to unconstrained problems but cannot apply to the more general cases where some variables of interest are subject to certain constraints. In this paper, we propose Differentiable Linearized ADMM (D-LADMM) for solving the problems with linear constraints. Specifically, D-LADMM is a K-layer LADMM inspired deep neural network, which is obtained by firstly introducing some learnable weights in the classical Linearized ADMM algorithm and then generalizing the proximal operator to some learnable activation function. Notably, we rigorously prove that there exist a set of learnable parameters for D-LADMM to generate globally converged solutions, and we show that those desired parameters can be attained by training D-LADMM in a proper way. To the best of our knowledge, we are the first to provide the convergence analysis for the learning-based optimization method on constrained problems.