Year: 2025
Type: article
Abstract: The continuous-time analysis of iterative algorithms for optimization has a long-standing history. This work introduces a novel framework for equality-constrained optimization based on control theory. The central concept is to design a feedback control system in which the Lagrange multipliers serve as the control inputs while the output represents the constraints. This system converges to a stationary point of the constrained optimization problem through suitable regulation. Concerning the Lagrange multipliers, we explore two control laws: proportional-integral control and feedback linearization. These choices lead to a variety of different methods. We rigorously develop the related algorithms, analyze their convergence theoretically, and present several numerical experiments that demonstrate their effectiveness compared to the state-of-the-art approaches.
Institution: Politecnico di Torino
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410226385