A distributed simplex algorithm for degenerate linear programs and multi-agent assignments

Authors:
Mathias BüRger;Giuseppe Notarstefano;Francesco Bullo;Frank AllgöWer
Affiliations:
Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany;Department of Engineering, University of Lecce, Via per Monteroni, 73100 Lecce, Italy;Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, CA 93106, USA;Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

In this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous peer-to-peer networks with distributed information structures. We propose a distributed version of the well-known simplex algorithm for general degenerate linear programs. A network of agents, running our algorithm, will agree on a common optimal solution, even if the optimal solution is not unique, or will determine infeasibility or unboundedness of the problem. We establish how the multi-agent assignment problem can be efficiently solved by means of our distributed simplex algorithm. We provide simulations supporting the conjecture that the completion time scales linearly with the diameter of the communication graph.