This paper studies edge caching in fog computing networks, where a
capacity-aware edge caching framework is proposed by considering both the
limited fog cache capacity and the connectivity capacity of base stations
(BSs). By allowing cooperation between fog nodes and cloud data center, the
average-download-time (ADT) minimization problem is formulated as a multi-class
processor queuing process. We prove the convexity of the formulated problem and
propose an Alternating Direction Method of Multipliers (ADMM)-based algorithm
that can achieve the minimum ADT and converge much faster than existing
algorithms. Simulation results demonstrate that the allocation of fog cache
capacity and connectivity capacity of BSs needs to be balanced according to the
network status. While the maximization of the edge-cache-hit-ratio (ECHR) by
utilizing all available fog cache capacity is helpful when the BS connectivity
capacity is sufficient, it is preferable to keep a lower ECHR and allocate more
traffic to the cloud when the BS connectivity capacity is deficient.

研究雾计算网络中的边缘缓存，通过考虑有限的雾缓存容量和基站连接容量，提出了一个容量感知的边缘缓存框架，并通过允许雾节点和云数据中心的协作来将平均下载时间（ADT）最小化， 通过多类处理器排队过程将此问题建模，提出了一种基于 ADMM 的算法，可实现最小化 ADT 并比现有算法更快地收敛。模拟结果表明，根据网络状态需要平衡雾缓存容量和基站连接能力的分配。当基站连接容量足够时，利用所有可用的雾缓存容量最大化边缘缓存命中率（ECHR）是有帮助的，但当基站连接容量不足时，最好保持较低的 ECHR 并将更多流量分配给云。

雾计算网络中的容量感知边缘缓存

Capacity-Aware Edge Caching in Fog Computing Networks

This work studies the denoising of piecewise smooth graph signals that
exhibit inhomogeneous levels of smoothness over a graph, where the value at
each node can be vector-valued. We extend the graph trend filtering framework
to denoising vector-valued graph signals with a family of non-convex
regularizers, which exhibit superior recovery performance over existing convex
regularizers. Using an oracle inequality, we establish the statistical error
rates of first-order stationary points of the proposed non-convex method for
generic graphs. Furthermore, we present an ADMM-based algorithm to solve the
proposed method and establish its convergence. Numerical experiments are
conducted on both synthetic and real-world data for denoising, support
recovery, event detection, and semi-supervised classification.

本研究研究了分段平滑图信号的去噪问题，使用非凸正则化器对值为向量的图信号进行了扩展，提高了恢复性能。提出了基于 ADMM 的算法来解决问题和证明了其收敛性。

非凸惩罚的矢量图趋势滤波

Vector-Valued Graph Trend Filtering with Non-Convex Penalties

We consider the stochastic composition optimization problem proposed in
\cite{wang2017stochastic}, which has applications ranging from estimation to
statistical and machine learning. We propose the first ADMM-based algorithm
named com-SVR-ADMM, and show that com-SVR-ADMM converges linearly for strongly
convex and Lipschitz smooth objectives, and has a convergence rate of $O( \log
S/S)$, which improves upon the $O(S^{-4/9})$ rate in
\cite{wang2016accelerating} when the objective is convex and Lipschitz smooth.
Moreover, com-SVR-ADMM possesses a rate of $O(1/\sqrt{S})$ when the objective
is convex but without Lipschitz smoothness. We also conduct experiments and
show that it outperforms existing algorithms.

针对随机分布式优化问题，提出 ADMM 算法，收敛速率为 O (1/logS), 并在实验中表现良好。