Contractivity of Distributed Optimization and Nash Seeking Dynamics
arXiv:2309.05873
Abstract
In this letter, we study distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, for distributed gradient flows based upon incidence and Laplacian constraints over arbitrary topologies, we establish strong contractivity over an appropriate invariant vector subspace. Third, we give sufficient conditions for strong contractivity in pseudogradient and best response games with complete information, show the equivalence of these conditions, and consider the special case of aggregative games.
7 pages, 1 figure, jointly submitted to the IEEE Control Systems Letters and the 2024 American Control Conference