Dual Smoothing for Decentralized Optimization

TL;DR

This paper introduces a dual smoothing technique to address non-smooth, non-strongly convex decentralized optimization problems, applicable to consensus and coupled constraints optimization, enhancing solution methods in distributed systems.

Contribution

The paper proposes a novel dual smoothing approach for decentralized optimization, specifically targeting non-smooth and non-strongly convex problems, and explores the duality between consensus and coupled constraints.

Findings

Effective smoothing of non-smooth problems

Duality between consensus and coupled constraints

Potential improvements in distributed optimization algorithms

Abstract

Decentralized optimization is widely used in different fields of study such as distributed learning, signal processing, and various distributed control problems. In these types of problems, nodes of the network are connected to each other and seek to optimize some objective function. In this article, we present a method for smoothing the non-smooth and non-strongly convex problems. This is done using the dual smoothing technique. We study two types of problems: consensus optimization of linear models and coupled constraints optimization. It is shown that these two problem classes are dual to each other.