Frequency-domain Analysis and Synthesis of Gradient-based Distributed Optimization Algorithms: A Robust Control Approach

Distributed optimization plays an essential role in large-scale engineering systems and complex networks, and is held as a key enabler to civil infrastructures and industrial systems. Driven by its widespread applications, in this project we launch a comprehensive investigation into the analysis and synthesis of distributed optimization algorithms. We aim to develop a general, systematic theory built on a novel frequency-domain framework, which has the unique, unequal advantage that allows us to exploit the insights and the varieties of time-honored frequency-domain techniques, in particular those of robust and optimal control, for the characterization, analysis, and design of fast, efficient, and robust distributed algorithms. Central to our development are four synergistic objectives, each of which contains a set of tasks, consisting of (1) developing a systematic analysis and synthesis approach centered at a frequency-domain characterization of distributed optimization algorithms; (2) quantifying algorithm robustness and developing robust distributed optimization algorithms; (3) developing distributed optimization methods and algorithms for the training and optimization of machine learning models; (4) conducting benchmark simulations to validate the theoretical developments. The objectives target key issues and fundamental challenges facing distributed optimization, which together constitute a conceptual as well as a technical leap beyond the current state of the distributed optimization research. Built on the PI’s prior projects and ongoing work on networked control, multi-agent systems, and distributed optimization, a coherent technical approach has been carved out, which consists of concrete, realistic solution strategies that are believed to be both theoretically significant and practically feasible, and which has the promise to deliver measurable results of significance. We hold the viewpoint that the results generated from this project will lead to new and better understanding of distributed optimization problems, and to their improved design methods and algorithms, thus contributing to the advance and application of optimization theories and benefiting researchers and practicing engineers in broad engineering fields.