Optimization Algorithms as Uncertain Graded Dynamical Systems
Bryan Van Scoy · 2025
The interpretation of iterative optimization algorithms as dynamical systems has led to a variety of advances in their analysis and design using tools from control. In this paper, we identify a structure of dynamical systems that arises naturally in a variety of optimization algorithms, and we show how to take advantage of this structure in system analysis. In particular, first-order optimization algorithms consist of the gradient of the objective in feedback with graded dynamical systems, which are systems whose signal spaces decompose as direct sums that are not mixed by the system dynamics.