Distributed Mirror Descent Algorithm With Bregman Damping for Nonsmooth Constrained Optimization

IEEE TRANSACTIONS ON AUTOMATIC CONTROL(2023)

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摘要
To efficiently solve the nonsmooth distributed optimization with both local constraints and coupled constraints, we propose a distributed continuous-time algorithm based on the mirror descent (MD) method. In this article, we introduce the Bregman damping into distributed MD-based dynamics, which not only successfully applies the MD idea to the distributed primal-dual framework, but also ensures the boundedness of all variables and the convergence of the entire dynamics. Our approach generalizes the classic distributed projection-based dynamics, and establishes a connection between MD methods and distributed Euclidean-projected approaches. Also, we prove the convergence of the proposed distributed dynamics with an O(1/t) rate. For practical implementation, we further give a discrete-time algorithm based on the proposed dynamics with an O(1/root k) convergence rate.
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关键词
Constrained optimization,distributed algorithm,mirror descent,multi-agent system,nonsmooth.
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