# A Unified Distributed Method for Constrained Networked Optimization via Saddle-Point Dynamics

arXiv: https://arxiv.org/abs/2307.07318 · HTML: https://mlsanity.com/paper/2307.07318/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2023.

## Built on by (most cited first, 3 of 3)

- [Energy-Aware Reinforcement Learning for Robotic Manipulation of Articulated Components in Infrastructure Operation and Maintenance](https://mlsanity.com/paper/2602.12288/) (2026)
- [Accelerated Stochastic Min-Max Optimization Based on Bias-corrected Momentum](https://mlsanity.com/paper/2406.13041/) (2024)
- [Asymmetric regularization mechanism for GAN training with Variational Inequalities](https://mlsanity.com/paper/2601.13920/) (2026)

## Abstract (arXiv)

This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform these two constrained networked optimization problems into a unified saddle-point problem framework with set constraints. Subsequently, two projection-based primal-dual algorithms via Optimistic Gradient Descent Ascent (OGDA) method and Extra-gradient (EG) method are developed for solving constrained saddle-point problems. It is shown that the developed algorithms achieve exact convergence to a saddle point with an ergodic convergence rate O(1/k) for general convex-concave functions. Based on the proposed primal-dual algorithms via saddle-point dynamics, we develop unified distributed algorithm design and convergence analysis for these two networked optimization problems. Finally, two numerical examples are presented to demonstrate the theoretical results.