2023/09/11 by Anand Gokhale, Gokhale, Anand, Alexander A. Davydov +3
Decision Sciences · Mathematics · Medicine · #FOS: Electrical engineering #FOS: Mathematics #Game Theory and Applications #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2309.05873
openalex publication_date 2023/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.