Distributed Subgradient Projection Algorithm over Directed Graphs: Alternate Proof

TL;DR

This paper introduces a distributed subgradient algorithm for multi-agent networks with directed communication graphs, achieving convergence in constrained convex optimization problems.

Contribution

It presents the D-DPS algorithm with an alternate proof, handling directed graphs and providing convergence rate analysis.

Findings

Convergence rate of O(ln k / sqrt(k)) established

Algorithm effectively manages directed communication asymmetry

Applicable to constrained convex optimization in multi-agent systems

Abstract

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 \emph{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 $O(\frac{\ln k}{\sqrt{k}})$.