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Home | Seminars and Symposia | Past seminars/symposia: Thursday, December 10, 2015

DTC Seminar Series

Prediction-Correction Methods for Time-Varying Optimization


Geert Leus
Delft University of Technology

Thursday, December 10, 2015
1:30 p.m.

402 Walter Library

Geert Leus

This talk covers unconstrained convex optimization problems with time-varying objective functions, which appear in controls and in large-scale power and communication networks for instance. We propose algorithms with a discrete-time sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate 1/h, where h is the step size. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists of either one or multiple gradient steps or Newton steps. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as quadratic in h, and in some cases even as quartic in h, which outperforms the state-of-the-art error bound for correction-only methods in the gradient-correction step, which is only linear in h. We do not only discuss centralized implementations, but also focus on distributed versions of these algorithms. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.


Geert Leus received the MSc and PhD degree in applied sciences from the Katholieke Universiteit Leuven, Belgium, in 1996 and 2000, respectively. Currently, Geert Leus is an "Antoni van Leeuwenhoek" Full Professor at the Faculty of Electrical Engineering, Mathematics and Computer Science of the Delft University of Technology, The Netherlands. His research interests are in the area of signal processing for communications. Geert Leus received a 2002 IEEE Signal Processing Society Young Author Best Paper Award and a 2005 IEEE Signal Processing Society Best Paper Award. He is a Fellow of the IEEE. Geert Leus was the Chair of the IEEE Signal Processing for Communications and Networking Technical Committee, and an Associate Editor for the IEEE Transactions on Signal Processing, the IEEE Transactions on Wireless Communications, the IEEE Signal Processing Letters, and the EURASIP Journal on Advances in Signal Processing. Currently, he is a Member-at-Large to the Board of Governors of the IEEE Signal Processing Society and a member of the IEEE Sensor Array and Multichannel Technical Committee. He finally serves as the Editor in Chief of the EURASIP Journal on Advances in Signal Processing.