UCSD

Mechanical and Aerospace Engineering

• Home
• Publications
• Group
• Teaching
• Software
• Lab

---

Saddle-point dynamics: conditions for asymptotic stability of saddle points
A. Cherukuri, B. Gharesifard, J. Cortés
SIAM Journal on Control and Optimization 55 (1) (2017), 486-511

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.

pdf   |   ps.gz

Mechanical and Aerospace Engineering, University of California, San Diego
9500 Gilman Dr, La Jolla, California, 92093-0411

Ph: 1-858-822-7930
Fax: 1-858-822-3107

cortes at ucsd.edu
Skype id: jorgilliyo