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• W1571174635 abstract "This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics (gradient-descent in the first variable and gradient-ascent in the second one). We identify a suite of complementary conditions under which the set of saddle points is asymptotically stable under the saddle-point dynamics. Our first set of results is based on the convexity-concavity of the function defining the saddle-point dynamics to establish the convergence guarantees. For functions that do not enjoy this feature, our second set of results relies on properties of the linearization of the dynamics and the function along the proximal normals to the saddle set. We also provide global versions of the asymptotic convergence results. Various examples illustrate our discussion." @default.
• W1571174635 created "2016-06-24" @default.
• W1571174635 creator A5027913099 @default.
• W1571174635 creator A5035350909 @default.
• W1571174635 date "2015-07-01" @default.
• W1571174635 modified "2023-09-25" @default.
• W1571174635 title "Asymptotic stability of saddle points under the saddle-point dynamics" @default.
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• W1571174635 doi "https://doi.org/10.1109/acc.2015.7171030" @default.
• W1571174635 hasPublicationYear "2015" @default.
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