Saddle-point dynamics and necessary and sufficient conditions for convergence

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• Ioannis Lestas, University of Cambridge
• Wednesday 22 February 2023, 14:00-15:00
• 909b.

If you have a question about this talk, please contact Giordano Scarciotti.

Abstract: Finding the saddle point of a concave-convex function is a problem that has been widely studied in since the 1950s in diverse areas and forms the basis of many classes of distributed optimisation algorithms. Nevertheless, in broad classes of problems there are features that render the analysis of the asymptotic behaviour of saddle-point dynamics nontrivial. In particular, even though for a strictly concave-convex function convergence to a saddle-point via gradient dynamics is ensured, when this strictness is lacking, convergence is not guaranteed and oscillatory solutions can occur. Furthermore, when the subgradient method is used to restrict the dynamics in a convex domain, the dynamics become non-smooth in continuous time, thus increasing significantly the complexity in the analysis.

In this talk we provide an explicit characterization to the asymptotic behaviour of gradient dynamics for saddle-point problems. In particular, we show that despite the nonlinear and non-smooth character of these dynamics their omega-limit set is comprised of trajectories that solve only linear ODEs that can be explicitly characterized. These results are used to formulate corresponding convergence criteria and various examples will also be discussed.

Biography: Ioannis Lestas is a Professor of Control Engineering at the Department of Engineering, University of Cambridge. He received the B.A. (Starred First) and M.Eng. (Distinction) degrees in Electrical and Information Sciences and the Ph.D. in control theory from the University of Cambridge (Trinity College) in 2002 and 2007, respectively. His doctoral work was performed as a Gates Scholar. He has been a Junior Research Fellow of Clare College, University of Cambridge and he was awarded a five year Royal Academy of Engineering research fellowship. He is also the recipient of a five year ERC starting grant. He is currently serving as Associate Editor for the IEEE Transactions on Automatic Control and the IEEE Transactions on Smart Grid. His research interests include analysis and control of large-scale networks with applications in power systems and smart grids.

This talk is part of the Control and Power Seminars series.

This talk is included in these lists:

• 909b
• Andrea Picciau's list
• Control and Power Seminars

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