CAREER: From Shannon to TCP: Theory, Algorithms, and Applications of Nonlinear Optimization in Communication Systems

本研究旨在为通信系统的非线性优化建立新的理论基础，开发高效的分布式求解算法，并将这些方法应用于下一代宽带接入网络。一个重要的目标是通过与几家大公司的合作，将优雅的数学模型和分析转化为实际的通信系统设计，对经济和社会生活方式产生重大影响。此外，还开发了两门关于通信系统优化方法的新课程。这些课程采用即时教学方法和模块化结构，跨越电气工程、计算机科学和运筹学之间的学科边界，以及物理层和网络层之间的传统划分。调查利用非线性优化的最新发展，解决通信系统分析和设计中比传统线性规划方法所允许的更广泛的问题，触及分层网络体系结构的每一层，对现实世界的部署产生实际影响，并为通信系统带来新的智力基础。在无线和有线通信中的几个不可或缺和相互依赖的领域，有两个主要的研究重点。首先是用最优化方法描述和计算的信息论极限。研究人员开发了一种拉格朗日对偶方法来证明、界定和计算单终端和多终端系统的信道容量和速率失真函数。二是效用最大化框架下的网络资源分配，包括分析了网络拥塞控制的Internet协议以及它与其他协议之间的交互，作为解决隐式网络效用最大化问题的分布式算法。“分层作为优化分解”的方法是为了对通信网络中不同的问题提供一个统一的观点。

This research aims at establishing new theoretical foundations for nonlinear optimization of communication systems, developing efficient and distributed solution algorithms, and applying the methodologies to enable next generation broadband access networks. An important goal is to transfer the elegance of mathematical models and analysis to practical communication system design, with significant impacts on economics and ways-of-life in the society through collaboration with several major companies. Furthermore, two new courses are developed on optimization methodologies for communication systems. Using a just-in-time pedagogical approach and a modular structure, these courses traverse the disciplinary boundaries among electrical engineering, computer science, and operations research, and the traditional divide between physical layer and networking layers.The investigation utilizes the power of recent developments in nonlinear optimization to tackle a much wider scope of problems in the analysis and design of communication systems than what the traditional linear programming methodologies allow, touching every layer of the layered network architecture, making practical impacts to real world deployments, and leading to a new intellectual foundation for communication systems. There are two major thrusts of research on several indispensable and interdependent areas in wireless and wired communications. First is information-theoretic limits characterized and computed using optimization methods. The investigator develops a Lagrange duality approach to prove, bound, and compute channel capacity and rate distortion functions for single and multiple terminal systems. Second is network resource allocation in the utility maximization framework, including analysis of Internet protocol of TCP congestion control and it's interact ional with other protocols as distributed algorithms solving implicit network utility maximization problems. The 'layering as optimization decomposition' approach is developed to provide a unified view on disparate problems in communication networks.