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Exponentially Convergent Algorithm Design for Constrained Distributed Optimization via Nonsmooth Approach
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DOI：10.1109/TAC.2021.3075666.png)
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Abstract
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We develop an exponentially convergent distributed algorithm to minimize a sum of nonsmooth cost functions with a set constraint. The set constraint generally leads to the nonlinearity in distributed algorithms, and results in difficulties to derive an exponential rate. In this article, we remove the consensus constraints by an exact penalty method, and then propose a distributed projected subgradient algorithm by virtue of a differential inclusion and a differentiated projection operator. Resorting to nonsmooth approaches, we prove the convergence for this algorithm, and moreover, provide both the sublinear and exponential rates under some mild assumptions.
Keywords:
Convergence
Distributed algorithms
Cost function
Heuristic algorithms
Resource management
Topology
Intelligent control
Constrained distributed optimization
exact penalty method
exponential convergence
nonsmooth approach
projected gradient dynamics
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