Decentralized Strongly-Convex Optimization with Affine Constraints: Primal and Dual Approaches

TL;DR

This paper explores decentralized optimization methods for strongly convex problems with affine constraints, presenting primal and dual approaches to improve understanding and solution strategies in distributed settings.

Contribution

It introduces primal and dual methods tailored for decentralized strongly convex optimization with affine constraints, extending existing theory to more complex constrained scenarios.

Findings

Developed primal and dual algorithms for affine-constrained decentralized optimization

Analyzed the theoretical properties and convergence of proposed methods

Extended the framework of decentralized optimization to include affine constraints

Abstract

Decentralized optimization is a common paradigm used in distributed signal processing and sensing as well as privacy-preserving and large-scale machine learning. It is assumed that several computational entities locally hold objective functions and are connected by a network. The agents aim to commonly minimize the sum of the local objectives subject by making gradient updates and exchanging information with their immediate neighbors. Theory of decentralized optimization is pretty well-developed in the literature. In particular, it includes lower bounds and optimal algorithms. In this paper, we assume that along with an objective, each node also holds affine constraints. We discuss several primal and dual approaches to decentralized optimization problem with affine constraints.