A Divide-and-Conquer Algorithm for Distributed Optimization on Networks

Abstract

In this paper, we consider networks with topologies described by some connected undirected graph G = (V, E) and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, and optimization problem minx F (x) = i∈V fi(x) with local objective functions fi depending only on neighboring variables of the vertex i ∈ V . We introduce a divide-and-conquer algorithm to solve the above optimization problem in a distributed and decentralized manner. The proposed divide-and-conquer algorithm has exponential convergence, its computational cost is almost linear with respect to the size of the network, and it can be fully implemented at fusion centers of the network. Our numerical demonstrations also indicate that the proposed divide-and-conquer algorithm has superior performance than popular decentralized optimization methods do for the least squares problem with/without 1 penalty.

CoDGraD: A Code-based Distributed Gradient Descent Scheme for Decentralized Convex Optimization

“…associated with the objective function f = m l=1 f l in (I.1) has been well studied, see [1,4,8,9,10,11,12,13,14,16,17,18] and references therein for various algorithms implementable in a strong fusion center or in local workers distributed over the network. Denote the gradient of g on R N by ∇g.…”