Newton-Raphson consensus for distributed convex optimization

May 16, 2014, Broida 1640

Luca Schenato

Padova University, Information Engineering


We address the problem of distributed unconstrained minimization of separable smooth convex cost functions, where the global cost is given by the sum of several local and private costs, each associated to a specific agent in a given communication network. Many applications fall within this framework such as robotic map-building, support vector machines, localization and smart-grid state estimation. We specifically propose a new technique called Newton-Raphson Consensus which merges linear consensus algorithms with Newton-Raphson ideas. The technique has the beneficial properties of requiring very little coordination and naturally supports time-varying topologies. We show that under suitable assumptions the proposed algorithm guarantees exponential convergence to the global minimum. Finally, we provide some numerical applications and comparisons with alternative strategies available in the literature such as ADMM and the Distributed Subgradient Methods.

Speaker's Bio

Luca Schenato is currently Associate Professor at the University of Padova. He received the Laurea Degree from the University of Padova in 1999 and the Ph.D. from UC Berkeley in 2003. He currently holds a visiting position at U.C. Berkeley. He was the recipient of the Italian Professorship "Returning Brains" in 2004, of the Eli Jury Award from the EECS Department of UC Berkeley in 2006, and of the EUCA European Control Award in 2014. His research interests include distributed control, estimation and optimization for multi-agent systems, control subject to communication constraints in networked control systems, and control of biomimetic locomotion. He was one of the organizers of the Conference on Robotics, Communication and Coordination (Robocomm) and the Workshop on Estimation and Control of Networked Systems (Necsys). He is member of IEEE and of the IFAC Technical Committee on "Networked Systems", and served as Associate Editor for the IEEE Transactions of Automatic Control.

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