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SHORT COURSE: Distributed Optimization in Networks

Start Date: February 15, 2016 2:00 PM
End Date: February 15, 2016 5:00 PM

Professor Angelia Nedich

University of Illinois​

The advances in wired and wireless technology necessitated the development of theory, models and tools to cope with new challenges posed by large-scale optimization problems over networks. The classical optimization works under the premise that all problem data is available to some central entity. This premise does not apply to large networked systems where typically each agent (node) in the network has access to its private local information and has a local view of the network only. The lecture will cover the development of such distributed computational models for time-varying networks. Distributed algorithms for convex constrained minimization and Nash-equilibrium problems will be considered including direct primal methods and primal-dual methods. The development of these methods combines optimization techniques with graph theory and the non-negative matrix theory, which model the network aspect. The lectures will provide some basic background theory on graphs, graph Laplacians and their properties, and the convergence results for stochastic matrix sequences. Using the graph models and optimization techniques, the convergence and convergence rate analysis of the methods will be presented, of which the convergence rate results will demonstrate the dependence of the method’s performance with respect to the problem and the network properties, such as the network capability to diffuse the information.

Bio: Angelia Nedich received her B.S. degree from the University of Montenegro (1987) and M.S. degree from the University of Belgrade (1990), both in Mathematics. She received her Ph.D. degrees from Moscow State University (1994) in Mathematics and Mathematical Physics, and from Massachusetts Institute of Technology in Electrical Engineering and Computer Science (2002). She has been at the BAE Systems Advanced Information Technology from 2002-2006. In Fall 2006, she has joined the Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champaign, USA.  She is a recipient of the NSF CAREER Award 2007 in Operations Research for her work in distributed multi-agent optimization. She has received the Donald Biggar Willett Scholar of Engineering Award (2013) and Dean’s Award for Excellence in Research (2015) from the College of Engineering at the University of Illinois at Urbana-Champaign.