The network utility maximization problem is the problem of maximizing the overall utility of a network under capacity constraints, where each source in the network has its own private nonsmooth concave utility function (which allows the true utility to be modeled accurately) and each link in the network has only its capacity constraint. To solve this problem, two distributed optimization algorithms are proposed: a projected proximal algorithm and a projected subgradient algorithm. These algorithms can be implemented for the case that each source tries to maximize only its utility by using its proximity operator or subdifferential and each link tries to satisfy only its capacity constraint by using the metric projection onto its capacity constraint set. A convergence analysis indicates that these algorithms are sufficient for each source to find the optimal resource allocation. The convergence, optimality, and performance of the proposed algorithms are demonstrated through numerical comparisons with the existing decentralized network flow control algorithm.

中文翻译：

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具有不平滑效用函数的网络资源分配的分布式优化

网络效用最大化问题是在容量限制下最大化网络的整体效用的问题，其中网络中的每个源都有其自己的私有非平滑凹效用函数（允许对真实效用进行精确建模），并且网络中的每个链路网络只有其容量限制。为了解决这个问题，提出了两种分布式优化算法：投影近端算法和投影次梯度算法。可以针对以下情况实现这些算法：每个源都尝试通过使用其接近算符或次微分来尝试仅最大化其效用，并且每个链接都尝试通过使用在其容量约束集上的度量投影来仅满足其容量约束。收敛分析表明，这些算法足以使每个资源找到最佳资源分配。通过与现有分散网络流量控制算法的数值比较，证明了所提算法的收敛性，最优性和性能。