# Distributed Subgradient Projection Algorithm over Directed Graphs: Alternate Proof

arXiv: https://arxiv.org/abs/1706.07707 · HTML: https://mlsanity.com/paper/1706.07707/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2017.

## Built on by (most cited first, 4 of 4)

- [Networked Signal and Information Processing](https://mlsanity.com/paper/2210.13767/) (2022)
- [Distributed Adaptive Learning Under Communication Constraints](https://mlsanity.com/paper/2112.02129/) (2021)
- [MUSIC: Accelerated Convergence for Distributed Optimization With Inexact and Exact Methods](https://mlsanity.com/paper/2403.02589/) (2024)
- [Using Non-Lipschitz Signum-based Functions for Distributed Optimization and Machine Learning: Trade-off Between Con-vergence Rate and Optimality Gap](https://mlsanity.com/paper/2608.01220/) (2026)

## Abstract (arXiv)

We propose Directed-Distributed Projected Subgradient (D-DPS) to solve a constrained optimization problem over a multi-agent network, where the goal of agents is to collectively minimize the sum of locally known convex functions. Each agent in the network owns only its local objective function, constrained to a commonly known convex set. We focus on the circumstance when communications between agents are described by a directed network. The D-DPS combines surplus consensus to overcome the asymmetry caused by the directed communication network. The analysis shows the convergence rate to be O(fracln k√k).