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In this paper, the distributed resource allocation problem on stronglyconnected and weight-balanced digraphs is investigated, where the decisions ofeach agent are restricted to satisfy the coupled network resource constraintsand heterogeneous general convex sets. Moreover, the local cost function can benon-smooth. In order to achieve the exact optimum of the nonsmooth resourceallocation problem, a novel continuous-time distributed algorithm based on thegradient descent scheme and differentiated projection operators is proposed.With the help of the set-valued LaSalle invariance principle and nonsmoothanalysis, it is demonstrated that the algorithm converges asymptotically to theglobal optimal allocation. Moreover, for the situation where local constraintsare not involved and the cost functions are differentiable with Lipschitzgradients, the convergence of the algorithm to the exact optimal solution isexponentially fast. Finally, the effectiveness of the proposed algorithms isillustrated by simulation examples.

Novel Distributed Algorithms Design for Nonsmooth Resource Allocation on Weight-Balanced Digraphs