Constrained Consensus and Alternating Projections
نویسنده
چکیده
We study the problem of reaching a consensus in the estimates of multiple agents forming a network with time-varying connectivity. Our main focus is on constrained consensus problems where the estimate of each agent is constrained to lie in a different closed convex constraint set. We consider a distributed “projected consensus algorithm” in which the local averaging operation is combined with projection onto the individual constraint sets. This algorithm can be viewed as an alternating projection method with weights that are varying over time and across agents. We study the convergence properties of the projected consensus algorithm. In particular, we show that under an interior point assumption, the estimates of each agent converge to the same vector, which lies in the intersection of the constraint sets.
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