The design of optimization algorithms has long been a matter of art, and it calls for systematic development of methods in which algorithms can be analyzed, designed, and benchmarked with regard to their key attributes such as efficiency, complexity, and robustness. Driven by prospects of ubiquitous applications critical to civil infrastructures and industrial systems, distributed optimization, widely considered the backbone of today’s large-scale engineering systems and complex networks, has received in the recent years considerable and increasing interest. Distributed optimization problems are typically posed in a setting of multi-agent systems, and distributed algorithms are sought after with the aim to achieve a global, common goal shared by all agents while the individual agents also seek to fulfill their own objectives.

In this talk I shall describe a control-theoretic, frequency-domain framework for the analysis and synthesis of distributed algorithms. Leveraged on the insights and the varieties of time-honored frequency-domain techniques, in particular those of robust and optimal control, we propose a general class of gradient-based distributed algorithms that can be characterized as an interconnected dynamical system consisting of a linear subsystem and a Lur’e type nonlinear component, which enables the analysis and synthesis of the algorithms from a robust control approach, facilitated by the circle criterion and the Zames–Falb theorem. By equating algorithm convergence with the absolute stability of the Lur’e system, the optimization of the algorithm convergence rate is recast as a Nevanlinna-Pick interpolation problem akin to one of H∞ optimal control. The solution to this latter problem leads to a variety of gradient-based algorithms of optimal and suboptimal convergence rates with algorithm complexity judiciously controlled.

Jie Chen holds the appointment of Chair Professor with the Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China. He received the B.S. degree in aerospace engineering from Northwestern Polytechnic University, Xian, China in 1982, the M.S.E. degree in electrical engineering, the M.A. degree in mathematics, and the Ph.D. degree in electrical engineering, all from The University of Michigan, Ann Arbor, Michigan, in 1985, 1987, and 1990, respectively. Prior to joining City University, he was with The University of California, Riverside, California from 1994 to 2014, where he was a Professor and served as Professor and Chair for the Department of Electrical Engineering. His main research interests are in the areas of linear multivariable systems theory, system identification, robust control, optimization, time-delay systems, networked control, and multi-agent systems.

He is the author of several books, on subjects ranging from system identification to time delay systems, and to information-theoretic control and fundamental control limitations. For his contributions he was elected a Fellow of IEEE, a Fellow of AAAS, a Fellow of IFAC, and a Fellow of SIAM. He was also recognized by the US National Science Foundation CAREER Award, Japan SICE International Award, and Natural Science Foundation of China Outstanding Overseas Young Scholar Award. He was an IEEE Control Systems Society Distinguished Lecturer.