Controlled multipliers optimization: a feedback control approach to constrained optimiation

After introducing the session by reviewing recent results on control-theoretic approaches to analysis and design of optimization algorithms, this tutorial talk introduces a novel framework for equality-constrained optimization based on control theory. The main idea 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 is forced to converge to a stationary point of the constrained optimization problem through suitable regulation of the Lagrange multipliers. More specifically, we present two control laws: proportional-integral control and feedback linearization that 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.