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Stability and instability in saddle point dynamics Part II: The subgradient method

Holding, T and Lestas, I Stability and instability in saddle point dynamics Part II: The subgradient method. IEEE Transactions on Automatic Control. ISSN 0018-9286 (Unpublished)

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Abstract

In part I we considered the problem of convergence to a saddle point of a concave-convex function in $C^2$ via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of subgradient dynamics that provide a restriction in a convex domain. We show that despite the nonlinear and non-smooth character of these dynamics their ω-limit set is comprised of solutions to only linear ODEs. In particular, we show that the latter are solutions to subgradient dynamics on affine subspaces which is a smooth class of dynamics the asymptotic properties of which have been exactly characterized in part I. Various convergence criteria are formulated using these results and several examples and applications are also discussed throughout the manuscript.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 22 Aug 2020 20:11
Last Modified: 02 Sep 2021 05:52
DOI: 10.1109/TAC.2020.3019381