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Mathematics > Optimization and Control

arXiv:2309.05873 (math)
[Submitted on 11 Sep 2023 (v1), last revised 21 Sep 2023 (this version, v2)]

Title:Contractivity of Distributed Optimization and Nash Seeking Dynamics

Authors:Anand Gokhale, Alexander Davydov, Francesco Bullo
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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.
Comments: 7 pages, 1 figure, jointly submitted to the IEEE Control Systems Letters and the 2024 American Control Conference
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
Cite as: arXiv:2309.05873 [math.OC]
  (or arXiv:2309.05873v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2309.05873

Submission history

From: Anand Gokhale [view email]
[v1] Mon, 11 Sep 2023 23:51:59 UTC (1,285 KB)
[v2] Thu, 21 Sep 2023 20:25:08 UTC (112 KB)
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