# NPGA: A Unified Algorithmic Framework for Decentralized Constraint-Coupled Optimization

arXiv: https://arxiv.org/abs/2205.11119 · HTML: https://mlsanity.com/paper/2205.11119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2022.

## Built on by (most cited first, 1 of 1)

- [A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks](https://mlsanity.com/paper/2508.20645/) (2025)

## Abstract (arXiv)

This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its theoretical convergence rate surpasses all known results. More importantly, NPGA serves not only as an algorithm but also as a unified algorithmic framework, encompassing various existing algorithms as special cases. By designing different network matrices, we can derive numerous versions of NPGA and analyze their convergences by leveraging the convergence results of NPGA conveniently, thereby enabling the design of more efficient algorithms. Finally, we conduct numerical experiments to compare the convergence rates of NPGA and existing algorithms, providing empirical evidence for the superior performance of NPGA.