TY - JOUR
T1 - Asynchronous broadcast-based convex optimization over a network
AU - Nedić, Angelia
N1 - Funding Information:
Manuscript received August 02, 2009; revised February 02, 2010, February 07, 2010, August 27, 2010, and September 03, 2010; accepted September 15, 2010. Date of publication September 27, 2010; date of current version June 08, 2011. This work was sponsored by the National Science Foundation under Grant CMMI-0742538. Recommended by Associate Editor F. Dabbene.
PY - 2011/6
Y1 - 2011/6
N2 - We consider a distributed multi-agent network system where each agent has its own convex objective function, which can be evaluated with stochastic errors. The problem consists of minimizing the sum of the agent functions over a commonly known constraint set, but without a central coordinator and without agents sharing the explicit form of their objectives. We propose an asynchronous broadcast-based algorithm where the communications over the network are subject to random link failures. We investigate the convergence properties of the algorithm for a diminishing (random) stepsize and a constant stepsize, where each agent chooses its own stepsize independently of the other agents. Under some standard conditions on the gradient errors, we establish almost sure convergence of the method to an optimal point for diminishing stepsize. For constant stepsize, we establish some error bounds on the expected distance from the optimal point and the expected function value. We also provide numerical results.
AB - We consider a distributed multi-agent network system where each agent has its own convex objective function, which can be evaluated with stochastic errors. The problem consists of minimizing the sum of the agent functions over a commonly known constraint set, but without a central coordinator and without agents sharing the explicit form of their objectives. We propose an asynchronous broadcast-based algorithm where the communications over the network are subject to random link failures. We investigate the convergence properties of the algorithm for a diminishing (random) stepsize and a constant stepsize, where each agent chooses its own stepsize independently of the other agents. Under some standard conditions on the gradient errors, we establish almost sure convergence of the method to an optimal point for diminishing stepsize. For constant stepsize, we establish some error bounds on the expected distance from the optimal point and the expected function value. We also provide numerical results.
KW - Asynchronous algorithms
KW - convex optimization
KW - distributed multi-agent system
KW - random broadcast network
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U2 - 10.1109/TAC.2010.2079650
DO - 10.1109/TAC.2010.2079650
M3 - Article
AN - SCOPUS:79958279921
SN - 0018-9286
VL - 56
SP - 1337
EP - 1351
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 6
M1 - 5585721
ER -