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Distributed optimization in an energy-constrained network using a digital communication scheme

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2 Author(s)
Razavi, A. ; Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN ; Zhi-Quan Luo

We consider a distributed optimization problem where n nodes, Sl, l isin {1,..., n}, wish to minimize a common strongly convex function f(x), x = [x1,..., xn]T , and suppose that node Sl only has control of variable xl. The nodes locally update their respective variables and periodically exchange their values over noisy channels. Previous studies of this problem have mainly focused on the convergence issue and the analysis of convergence rate. In this work, we focus on the communication energy and study its impact on convergence. In particular, we study the minimum amount of communication energy required for nodes to obtain an isin-minimizer of f(x) in the mean square sense. In an earlier work, we considered analog communication schemes and proved that the communication energy must grow at the rate of Omega(isin-1) to obtain an isin-minimizer of a convex quadratic function. In this paper, we consider digital communication schemes and propose a distributed algorithm which only requires communication energy of O ((log isin-1)3) to obtain an isin-minimizer of f(x). Furthermore, the algorithm provided herein converges linearly. Thus, distributed optimization with digital communication schemes is significantly more energy efficient than with analog communication schemes.

Published in:

Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on

Date of Conference:

19-24 April 2009