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SYTACom Seminar

On the Convergence of Limited Communications Gradient Methods with Applications to Resource Allocation in Power Networks

Sindri Magnússon
KTH Royal Institute of Technology

October 7, 2015 at  11:00 AM
McConnell Engineering Room 603


Distributed control and decision making increasingly play a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the full potential of the technology has not yet been fully exploited in practice due to communication limitations of real-world infrastructures. This work investigates the fundamental properties of gradient methods for distributed optimization, where gradient information is communicated at every iteration, when using limited number of communicated bits. In particular, a general class of quantized gradient methods are studied where the gradient direction is approximated by a finite quantization set. Conditions on the quantization set are provided that are necessary and sufficient to guarantee the ability of these methods to minimize any convex objective function with Lipschitz continuous gradient and a nonempty, bounded set of optimizers. Moreover, a lower bound on the cardinality of the quantization set is provided, along with specific examples of minimal quantizations. Furthermore, convergence rate results are established that connect the fineness of the quantization and number of iterations needed to reach a predefined solution accuracy. The results provide a bound on the number of bits needed to achieve the desired accuracy. Finally, an application of the theory to resource allocation in power networks is demonstrated, and the theoretical results are substantiated by way of numerical simulations.


Sindri Magnússon received the B.Sc. degree in Mathematics from University of Iceland, Reykjavik Iceland, in 2011, and the Master’s degree in Mathematics from KTH Royal Institute of Technology, Stockholm Sweden, in 2013. He is currently pursuing the PhD at the Department of Automatic Control, School of Electrical Engineering and ACCESS Linnaeus Center, KTH Royal Institute of Technology, Stockholm, Sweden. He has held a six-months visiting research position at Harvard University, Cambridge, MA (2015) sponsored by the Engblom Foundation. His research interests include distributed optimization, both theory and applications.