Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization

TL;DR

This paper introduces a consensus-based dual decomposition method for distributed convex optimization that eliminates the need for a central master node and provides a way for nodes to recover approximate primal solutions.

Contribution

It proposes a novel consensus-based dual decomposition scheme with primal recovery, removing the master node requirement in distributed convex optimization.

Findings

Achieves dual and primal convergence up to a bounded error floor.

Uses a constant stepsize for convergence.

Enables nodes to access approximate near-optimal primal solutions.

Abstract

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled, the dual decomposition scheme involves local parallel subgradient calculations and a global subgradient update performed by a master node. In this paper, we propose a consensus-based dual decomposition to remove the need for such a master node and still enable the computing nodes to generate an approximate dual solution for the underlying convex optimization problem. In addition, we provide a primal recovery mechanism to allow the nodes to have access to approximate near-optimal primal solutions. Our scheme is based on a constant stepsize choice and the dual and primal objective convergence are achieved up to a bounded error floor dependent on the stepsize and on the number of consensus steps among the nodes.