Decentralized Constrained Optimization: Double Averaging and Gradient Projection

TL;DR

This paper introduces a decentralized projected gradient method for convex constrained optimization over directed graphs, leveraging local averaging and smoothness to ensure convergence.

Contribution

It presents a novel decentralized algorithm for convex constrained problems on directed graphs, with convergence guarantees based solely on local smoothness.

Findings

The proposed method converges under standard smoothness assumptions.

It effectively handles constraints known only locally at each node.

The algorithm is suitable for large-scale distributed optimization.

Abstract

In this paper, we consider the convex, finite-sum minimization problem with explicit convex constraints over strongly connected directed graphs. The constraint is an intersection of several convex sets each being known to only one node. To solve this problem, we propose a novel decentralized projected gradient scheme based on local averaging and prove its convergence using only local functions' smoothness.