IEEE Trans Cybern. 2018 Nov;48(11):3116-3125. doi: 10.1109/TCYB.2017.2759141. Epub 2017 Oct 17.
In this paper, a distributed resource allocation problem with nonsmooth local cost functions is considered, where the interaction among agents is depicted by strongly connected and weight-balanced digraphs. Here the decision variable of each agent is within a local feasibility constraint described as a convex set, and all the decision variables have to satisfy a network resource constraint, which is the sum of available resources. To solve the problem, a distributed continuous-time algorithm is developed by virtue of differentiated projection operations and differential inclusions, and its convergence to the optimal solution is proved via the set-valued LaSalle invariance principle. Furthermore, the exponential convergence of the proposed algorithm can be achieved when the local cost functions are differentiable with Lipschitz gradients and there are no local feasibility constraints. Finally, numerical examples are given to verify the effectiveness of the proposed algorithms.
本文研究了具有非光滑局部代价函数的分布式资源分配问题，其中通过强连通且加权平衡的有向图来描述代理之间的相互作用。这里每个代理的决策变量在局部可行性约束内，该约束描述为一个凸集，并且所有决策变量都必须满足网络资源约束，即可用资源的总和。为了解决这个问题，通过微分投影操作和微分包含，开发了一种分布式连续时间算法，并通过集值 LaSalle 不变性原理证明了其收敛到最优解。此外，当局部代价函数具有 Lipschitz 梯度且没有局部可行性约束时，该算法可以达到指数收敛。最后，给出了数值示例以验证所提出算法的有效性。
