# Federated Smoothing ADMM for Localization

arXiv: https://arxiv.org/abs/2503.09497 · HTML: https://mlsanity.com/paper/2503.09497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Federated Learning for Computationally-Constrained Heterogeneous Devices: A Survey](https://mlsanity.com/paper/2307.09182/) (2023)
- [Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties](https://mlsanity.com/paper/2309.03094/) (2023)
- [Decentralized Smoothing ADMM for Quantile Regression with Non-Convex Sparse Penalties](https://mlsanity.com/paper/2408.01307/) (2024)
- [Robust Networked Federated Learning for Localization](https://mlsanity.com/paper/2308.16737/) (2023)

## Abstract (arXiv)

This paper addresses the challenge of localization in federated settings, which are characterized by distributed data, non-convexity, and non-smoothness. To tackle the scalability and outlier issues inherent in such environments, we propose a robust algorithm that employs an ℓ1-norm formulation within a novel federated ADMM framework. This approach addresses the problem by integrating an iterative smooth approximation for the total variation consensus term and employing a Moreau envelope approximation for the convex function that appears in a subtracted form. This transformation ensures that the problem is smooth and weakly convex in each iteration, which results in enhanced computational efficiency and improved estimation accuracy. The proposed algorithm supports asynchronous updates and multiple client updates per iteration, which ensures its adaptability to real-world federated systems. To validate the reliability of the proposed algorithm, we show that the method converges to a stationary point, and numerical simulations highlight its superior performance in convergence speed and outlier resilience compared to existing state-of-the-art localization methods.