This paper presents a decentralized algorithm for solving distributed convex optimization problems in dynamic networks with time-varying objectives. The unique feature of the algorithm lies in its ability to accommodate a wide range of communication systems, including previously unsupported ones, by abstractly modeling the information exchange in the network. Specifically, it supports a novel communication protocol based on the "over-the-air" function computation (OTA-C) technology, that is designed for an efficient and truly decentralized implementation of the consensus step of the algorithm. Unlike existing OTA-C protocols, the proposed protocol does not require the knowledge of network graph structure or channel state information, making it particularly suitable for decentralized implementation over ultra-dense wireless networks with time-varying topologies and fading channels. Furthermore, the proposed algorithm synergizes with the "superiorization" methodology, allowing the development of new distributed algorithms with enhanced performance for the intended applications. The theoretical analysis establishes sufficient conditions for almost sure convergence of the algorithm to a common time-invariant solution for all agents, assuming such a solution exists. Our algorithm is applied to a real-world distributed random field estimation problem, showcasing its efficacy in terms of convergence speed, scalability, and spectral efficiency. Furthermore, we present a superiorized version of our algorithm that achieves faster convergence with significantly reduced energy consumption compared to the unsuperiorized algorithm.

翻译：本文提出一种面向动态网络与时变目标的分布式凸优化问题求解算法。该算法的独特之处在于，通过对网络中信息交换过程进行抽象建模，能够适应包括此前未支持系统在内的各类通信系统。具体而言，本算法支持基于“空口”函数计算（OTA-C）技术的新型通信协议，该协议专为算法共识步骤的高效、真正去中心化实现而设计。与现有OTA-C协议不同，本文所提协议无需预设网络拓扑结构或信道状态信息，特别适用于存在时变拓扑与衰落信道的超密集无线网络中的去中心化实现。此外，该算法与“超优化”方法协同作用，可为目标应用开发性能更优的新颖分布式算法。理论分析建立了算法在几乎所有情况下收敛至所有智能体共同时不变解的充分条件（假设该解存在）。我们将算法应用于实际分布式随机场估计问题，展示了其在收敛速度、可扩展性与频谱效率方面的有效性。进一步地，本文提出超优化版本算法，相较原始算法在显著降低能耗的同时实现更快收敛。