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

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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.