Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Asymptotic stability of saddle points under the saddle-point dynamics
A. Cherukuri, J. Cortés
Proceedings of the American Control Conference, Chicago, Illinois, USA, 2015, pp. 2020-2025
2015 ACC Best Student Paper Award Finalist
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.
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Mechanical and Aerospace Engineering,
University of California, San Diego
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