We present a simple decentralized algorithm to solve optimization problems involving cooperative agents. Cooperative agents share a common objective and simultaneously pursue private goals. Furthermore, agents are constrained by limited communication capabilities. The algorithm is based on dual decomposition techniques and appears to be very intuitive. It solves the dual problem of an artificially decomposed version of the primal problem, replacing one large computationally intractable problem with many smaller tractable problems. It returns a feasible solution to the primal problem as well as an upper bound on the distance between this solution and the global optimum. Both convex and nonconvex examples of multiple interacting aircraft are presented.
In the second part of the talk, the methodology is extended to treat competitive agents in a market, and is applied to multiple, competing airlines in the National Airspace System.
Joint work with Robin Raffard, Steven Waslander, and Stephen Boyd.
Audio (MP3 File, Podcast Ready)
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