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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1793291, 13 pages
Research Article

Distributed Constrained Stochastic Subgradient Algorithms Based on Random Projection and Asynchronous Broadcast over Networks

1State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, China
2Information Engineering College, Henan University of Science and Technology, Luoyang, China

Correspondence should be addressed to Junlong Zhu

Received 22 February 2017; Accepted 17 July 2017; Published 28 September 2017

Academic Editor: Thomas Hanne

Copyright © 2017 Junlong Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a distributed constrained optimization problem over a time-varying network, where each agent only knows its own cost functions and its constraint set. However, the local constraint set may not be known in advance or consists of huge number of components in some applications. To deal with such cases, we propose a distributed stochastic subgradient algorithm over time-varying networks, where the estimate of each agent projects onto its constraint set by using random projection technique and the implement of information exchange between agents by employing asynchronous broadcast communication protocol. We show that our proposed algorithm is convergent with probability 1 by choosing suitable learning rate. For constant learning rate, we obtain an error bound, which is defined as the expected distance between the estimates of agent and the optimal solution. We also establish an asymptotic upper bound between the global objective function value at the average of the estimates and the optimal value.