Abstract:
This paper studies the projected saddle-point dynamics for a twice differentiable convex-concave function, which we term saddle function. The dynamics consists of gradien...Show MoreMetadata
Abstract:
This paper studies the projected saddle-point dynamics for a twice differentiable convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We provide a novel characterization of the omega-limit set of the trajectories of these dynamics in terms of the diagonal Hessian blocks of the saddle function. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexity-concavity of the saddle function. If this property is global, and for the case when the saddle function takes the form of the Lagrangian of an equality constrained optimization problem, we establish the input-to-state stability of the saddle-point dynamics by providing an ISS Lyapunov function. Various examples illustrate our results.
Published in: 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Date of Conference: 27-30 September 2016
Date Added to IEEE Xplore: 13 February 2017
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