A control perspective for centralized and distributed convex optimization

TLDR

The control system viewpoint offers many insights and new research directions. The paper investigates how natural and engineered systems can perform complex optimizations with limited computational and communication resources, and proposes a general control‑system‑based framework to design distributed optimization algorithms that converge to convex problem solutions. The authors adopt a continuous‑time dynamical system perspective, merging early optimization theory with network protocol design and distributed averaging, and apply this framework to a distributed optimal location problem to illustrate its tracking and adaptation capabilities. Applying the framework to a distributed optimal location problem shows that the system can naturally track and adapt to changing constraints.

Abstract

In this paper, we want to study how natural and engineered systems could perform complex optimizations with limited computational and communication capabilities. We adopt a continuous-time dynamical system view rooted in early work on optimization and more recently in network protocol design, and merge it with the dynamic view of distributed averaging systems. We obtain a general approach, based on the control system viewpoint, that allows to analyze and design (distributed) optimization systems converging to the solution of given convex optimization problems. The control system viewpoint provides many insights and new directions of research. We apply the framework to a distributed optimal location problem and demonstrate the natural tracking and adaptation capabilities of the system to changing constraints.