An approximate projection algorithm for distributed set intersection computation

In this paper, we propose an approximate projection algorithm for a multi-agent network to cooperatively compute the intersection of hollow convex sets with switching topologies. This problem is equivalent to a non-convex constrained intersection computation problem, which can be converted into a convex constrained weighted optimization problem. We allow the presence of some computation errors for each agent to compute projections with respect to its own small set. We show that, with some appropriately selected projection accuracy conditions, all agents converge to the same point in the intersection set of a group of hollow convex sets. In addition, we prove that this point is the optimal solution of the proposed convex constrained weighted optimization problem.