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• W4200000914 abstract "In this paper, two distributed multi-proximal primal–dual algorithms are proposed to deal with a class of distributed nonsmooth resource allocation problems. In these problems, the global cost function is the summation of local convex and nonsmooth cost functions, each of which consists of one twice differentiable function and multiple nonsmooth functions. Communication graphs of underlying multi-agent systems are directed and strongly connected but not necessarily weighted-balanced. The multi-proximal splitting is introduced to deal with the difficulty caused by the unproximable property of the summation of those nonsmooth functions. Moreover, it can also guarantee the Lipschitz continuity of proposed algorithms. Auxiliary variables in the multi-proximal splitting are designed to estimate subgradients of nonsmooth functions. Theoretically, the convergence analysis is conducted by employing Lyapunov stability theory and integral input-to-state stability (iISS) theory with respect to sets. It shows that proposed algorithms converge to the optimal point while satisfying resource allocation constraints." @default.
• W4200000914 created "2021-12-31" @default.
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• W4200000914 date "2022-02-01" @default.
• W4200000914 modified "2023-10-16" @default.
• W4200000914 title "Solving a class of nonsmooth resource allocation problems with directed graphs through distributed Lipschitz continuous multi-proximal algorithms" @default.
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• W4200000914 doi "https://doi.org/10.1016/j.automatica.2021.110071" @default.
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