Lyapunov Approach to Consensus Problems
Abstract:
This talk is focused on the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the behavior of weighted-averaging dynamic. As a result, new convergence rate results are obtained that capture the graph structure in a novel way. In particular, the exponential convergence rate is established for unconstrained consensus with the exponent of the order of O(1/(mlog2m)). Also, the exponential convergence rate is established for constrained consensus, which extends the existing results limited to the use of doubly stochastic weight matrices.
Biography:
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. In 2013, she has received the Donald Biggar Willett Scholar of Engineering award from the College of Engineering at the University of Illinois at Urbana-Champaign.
Her general interest is in optimization and dynamics including fundamental theory, models, algorithms, and applications. Her current research interest is focused on large-scale convex optimization, distributed multi-agent optimization and equilibrium problems, stochastic approximations, and network aggregation-dynamics with applications in signal processing, machine learning, and decentralized control.