# Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems

arXiv: https://arxiv.org/abs/1302.0756 · HTML: https://mlsanity.com/paper/1302.0756/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2013.

## Built on by (most cited first, 7 of 7)

- [Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity](https://mlsanity.com/paper/2112.01939/) (2021)
- [Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling](https://mlsanity.com/paper/2105.01853/) (2021)
- [Symbiotic Agents: A Novel Paradigm for Trustworthy AGI-driven Networks](https://mlsanity.com/paper/2507.17695/) (2025)
- [Hyperparameter Estimation for Sparse Bayesian Learning Models](https://mlsanity.com/paper/2401.02544/) (2024)
- [Efficient Wireless Federated Learning via Low-Rank Gradient Factorization](https://mlsanity.com/paper/2401.07496/) (2024)
- [RIS-Enabled Smart Wireless Environments: Fundamentals and Distributed Optimization](https://mlsanity.com/paper/2512.18788/) (2025)
- [Operational Regimes in Non-Convex Optimization: A Multiplier-Based Taxonomy](https://mlsanity.com/paper/2609.00471/) (2026)

## Abstract (arXiv)

We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multiuser interfering systems. Our main contributions are: i) the development of the first class of (inexact) Jacobi best-response algorithms with provable convergence, where all the users simultaneously and iteratively solve a suitably convexified version of the original sum-utility optimization problem; ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics; and iii) a framework that can be easily particularized to well-known applications, giving rise to very efficient practical (Jacobi or Gauss-Seidel) algorithms that outperform existing adhoc methods proposed for very specific problems. Interestingly, our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many blockcoordinate descent schemes for convex functions.