Abstract
This paper considers a distributed nonsmooth resource allocation problem of minimizing a global convex function formed by a sum of local nonsmooth convex functions with coupled constraints. A distributed communication-efficient mirror-descent algorithm, which can reduce communication rounds between agents over the network, is designed for the distributed resource allocation problem. By employing communication-sliding methods, agents can find a ε-solution in \(O\left( {{1 \over \varepsilon }} \right)\) communication rounds while maintaining \(O\left( {{1 \over {{\varepsilon ^2}}}} \right)\) subgradient evaluations for nonsmooth convex functions. A numerical example is also given to illustrate the effectiveness of the proposed algorithm.
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 72101026, 61621063, and the State Key Laboratory of Intelligent Control and Decision of Complex Systems.
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Wang, Y., Tu, Z. & Qin, H. Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem. J Syst Sci Complex 35, 1244–1261 (2022). https://doi.org/10.1007/s11424-022-0187-8
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DOI: https://doi.org/10.1007/s11424-022-0187-8