There has been much interest in distributed cooperative control problems, in which several autonomous agents collectively try to achieve a global objective. Most focus has been on the canonical consensus problem, where the goal is to develop distributed algorithms that can be used by a group of agents to reach a common decision or agreement. In this talk, we consider two important extensions of the consensus problem that address optimization of general convex objective functions and presence of constraints on decisions of agents.

We first use consensus algorithms to develop distributed subgradient methods for optimizing a sum of convex (not necessarily smooth) objective functions corresponding to multiple agents connected through a time-varying topology. We provide convergence results and convergence rate estimates for these methods. Our convergence rate results explicitly characterize the tradeoff between the desired accuracy of the generated approximate optimal solutions and the number of iterations needed to achieve the accuracy. Second, we consider constrained consensus problems where the decision of each agent is constrained to lie in a different closed convex constraint set. We present a distributed "projected consensus algorithm" for this problem. We make the connection of this algorithm to Von Neumann's alternating projection method and establish convergence and rate results.

This is joint work with Angelia Nedic (UIUC) and Pablo Parrilo (MIT).

BIO:
Asu Ozdaglar received the B.S. degree in electrical engineering from the Middle East Technical University, Ankara, Turkey, in 1996, and the S.M. and the Ph.D. degrees in electrical engineering and computer science from the Massachusetts Institute of Technology, Cambridge, in 1998 and 2003, respectively.

Since 2003, she has been a member of the faculty of the Electrical Engineering and Computer Science Department at the Massachusetts Institute of Technology, where she is currently the Class of 1943 Associate Professor. She is also a member of the Laboratory for Information and Decision Systems and the Operations Research Center. Her research interests include optimization theory, with emphasis on nonlinear programming and convex analysis, game theory, distributed optimization methods, and network optimization and control. She is the co-author (with Dimitri P. Bertsekas and Angelia Nedic) of the book entitled ¡°Convex Analysis and Optimization¡± (Athena Scientific, 2003). She is the recipient of a Microsoft fellowship, the MIT Graduate Student Council Teaching award, the NSF Career award, and the 2008 Donald P. Eckman award of the American Automatic Control Council.