Jorge Cortés
Professor
Cymer Corporation Endowed Chair
The role of strong convexity-concavity in the convergence and
robustness of the saddle-point dynamics
A. Cherukuri, E. Mallada, S. Low, J. Cortés
Allerton Conference on Communications, Control, and Computing,
Monticello, Illinois, USA, 2016, pp. 504-510
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.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
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cortes at ucsd.edu
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