Randomized Constraints Consensus for Distributed Robust Mixed-Integer Programming

In this article, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows common cost function and its local uncertain constraint set. We propose randomized, distributed algorithm working under asynchronous, unreliable, directed communication. The is based on computation communication paradigm. At each round, nodes perform two updates: 1) A verification in which they check-in randomized fashion-the robust feasibility candidate optimal point, 2) an optimization step exchange their basis (the minimal set constraints defining solution) with neighbors locally solve problem. As main result, show that can stop the after finite number rounds (either because has been successful for sufficient or given threshold reached) so solutions are consensual. solution proven be-with high confidence-feasible and, hence, entire uncertainty except subset having arbitrarily small probability measure. effectiveness proposed using examples: random, linear program localization wireless sensor networks. implemented multicore platform communicate asynchronously.