Mathematical optimization is now widely regarded as an indispensable modeling and solution tool for the design of wireless communications systems. While optimization has played a significant role in the revolutionary progress in wireless communication and networking technologies from 1G to 5G and onto the future 6G, the innovations in wireless technologies have also substantially transformed the nature of the underlying mathematical optimization problems upon which the system designs are based and have sparked significant innovations in the development of methodologies to understand, to analyze, and to solve those problems. In this paper, we provide a comprehensive survey of recent advances in mathematical optimization theory and algorithms for wireless communication system design. We begin by illustrating common features of mathematical optimization problems arising in wireless communication system design. We discuss various scenarios and use cases and their associated mathematical structures from an optimization perspective. We then provide an overview of recently developed optimization techniques in areas ranging from nonconvex optimization, global optimization, and integer programming, to distributed optimization and learning-based optimization. The key to successful solution of mathematical optimization problems is in carefully choosing or developing suitable algorithms (or neural network architectures) that can exploit the underlying problem structure. We conclude the paper by identifying several open research challenges and outlining future research directions.

中文翻译：

---

无线通信优化方法的最新进展综述


数学优化现在被广泛认为是无线通信系统设计中不可或缺的建模和求解工具。虽然优化在从 1G 到 5G 再到未来 6G 的无线通信和网络技术的革命性进步中发挥了重要作用，但无线技术的创新也极大地改变了系统设计所基于的基础数学优化问题的性质，并在开发理解方法方面引发了重大创新。 来分析并解决这些问题。在本文中，我们对无线通信系统设计的数学优化理论和算法的最新进展进行了全面调查。我们首先说明了无线通信系统设计中出现的数学优化问题的常见特征。我们从优化的角度讨论各种场景和用例及其相关的数学结构。然后，我们概述了最近开发的优化技术，从非凸优化、全局优化和整数规划到分布式优化和基于学习的优化。成功解决数学优化问题的关键是仔细选择或开发合适的算法（或神经网络架构），以利用底层问题结构。我们通过确定几个开放的研究挑战并概述未来的研究方向来结束本文。