Distributed Optimization Using the Primal-Dual Method of Multipliers

G. Zhang; R. Heusdens

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arXiv · 1702.00841

Distributed Optimization Using the Primal-Dual Method of Multipliers

G. Zhang·R. Heusdens

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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.

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BibTeX RIS

G. Zhang, R. Heusdens. 2017-02-02. Distributed Optimization Using the Primal-Dual Method of Multipliers. https://arxiv.org/abs/1702.00841

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