# Linearized ADMM for Non-convex Non-smooth Optimization with Convergence Analysis

arXiv: https://arxiv.org/abs/1705.02502 · HTML: https://mlsanity.com/paper/1705.02502/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2017.

## Built on by (most cited first, 12 of 12)

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- [Learning to Accelerate Approximate Methods for Solving Integer Programming via Early Fixing](https://mlsanity.com/paper/2207.02087/) (2022)
- [Provably Convergent Plug & Play Linearized ADMM, applied to Deblurring Spatially Varying Kernels](https://mlsanity.com/paper/2210.10605/) (2022)
- [A Simple Adaptive Unfolding Network for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2301.10208/) (2023)
- [A Convergent ADMM Framework for Efficient Neural Network Training](https://mlsanity.com/paper/2112.11619/) (2021)
- [Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints](https://mlsanity.com/paper/2201.07657/) (2022)
- [Differentially Private Neural Network Training Under the Hidden State Assumption](https://mlsanity.com/paper/2407.08233/) (2024)
- [Function-Space ADMM for Decentralized Federated Learning: A Control Theoretic Perspective](https://mlsanity.com/paper/2605.09356/) (2026)
- [Physics-Aware Linearized ADMM and Its Unrolling](https://mlsanity.com/paper/2606.01652/) (2026)

## Abstract (arXiv)

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its broad applications in nonconvex optimization, for a great number of nonconvex and nonsmooth objective functions, its theoretical convergence guarantee is still an open problem. In this paper, we propose a two-block linearized ADMM and a multi-block parallel linearized ADMM for problems with nonconvex and nonsmooth objectives. Mathematically, we present that the algorithms can converge for a broader class of objective functions under less strict assumptions compared with previous works. Furthermore, our proposed algorithm can update coupled variables in parallel and work for less restrictive nonconvex problems, where the traditional ADMM may have difficulties in solving subproblems.