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Distributed and time-varying primal-dual dynamics via contraction analysis

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Document pages: 18 pages

Abstract: In this note, we provide an overarching analysis of primal-dual dynamicsassociated to linear equality-constrained optimization problems usingcontraction analysis. For the well-known standard version of the problem: weestablish convergence under convexity and the contracting rate under strongconvexity. Then, for a canonical distributed optimization problem, we usepartial contractivity to establish global exponential convergence of itsprimal-dual dynamics. As an application, we propose a new distributed solverfor the least-squares problem with the same convergence guarantees. Finally,for time-varying versions of both centralized and distributed primal-dualdynamics, we exploit their contractive nature to establish bounds on theirtracking error. To support our analyses, we introduce novel results oncontraction theory.

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