Distributed Optimization Using the Primal-Dual Method of Multipliers
Abstract
In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear equality constraint. In designing the new algorithm, an augmented primal-dual Lagrangian function is constructed which smoothly captures the graph topology. It is shown that a saddle point of the constructed function provides an optimal solution of the original problem. Further under both the synchronous and asynchronous updating schemes, PDMM has the convergence rate of O(1/K) (where K denotes the iteration index) for general closed, proper and convex functions. Other properties of PDMM such as convergence speeds versus different parameter- settings and resilience to transmission failure are also investigated through the experiments of distributed averaging.
Cite
@article{arxiv.1702.00841,
title = {Distributed Optimization Using the Primal-Dual Method of Multipliers},
author = {G. Zhang and R. Heusdens},
journal= {arXiv preprint arXiv:1702.00841},
year = {2017}
}