In this paper, a general nonlinear 1st-order consensus-based solution for distributed constrained convex optimization is considered for applications in network resource allocation. The proposed continuous-time solution is used to optimize continuously-differentiable strictly convex cost functions over weakly-connected undirected multi-agent networks. The solution is anytime feasible and models various nonlinearities to account for imperfections and constraints on the (physical model of) agents in terms of their limited actuation capabilities, e.g., quantization and saturation constraints among others. Moreover, different applications impose specific nonlinearities to the model, e.g., convergence in fixed/finite-time, robustness to uncertainties, and noise-tolerant dynamics. Our proposed distributed resource allocation protocol generalizes such nonlinear models. Putting convex set analysis together with the Lyapunov theorem, we provide a general technique to prove convergence (i) regardless of the particular type of nonlinearity (ii) with weak network-connectivity requirement (i.e., uniform-connectivity). We simulate the performance of the protocol in continuous-time coordination of generators, known as the economic dispatch problem (EDP).

翻译：在本文中,在网络资源分配的应用中,考虑对分布式受限制的锥形优化采用一般非线性1级协商一致解决办法。拟议的连续时间解决办法用于优化对连接薄弱、无源的多试剂网络的连续、严格分解的成本功能;这一解决办法在时间上是可行的,并模拟各种非线性办法,以说明(物理模型)代理人的不完善和限制,即作用能力有限,例如,四分化和饱和等限制。此外,不同的应用办法对模型规定了具体的非线性,例如固定/固定时间的趋同、对不确定性的稳健性和噪音容忍动态。我们拟议的分布式资源分配协议对非线性模式作了一般性的介绍。将配置式分析与Lyapunovsorem结合起来,我们提供了一种一般技术,证明(一) 不论非线性的具体类型(二) 网络连接性弱(即经济连接性)。我们用连续时间协调发电机的问题来模拟协议的履行情况。