Constrained Optimization From a Control Perspective via Feedback Linearization

Runyu Zhang, Arvind Raghunathan, Jeff S Shamma, Na Li

TL;DR: We study theoretical foundations for applying Feedback Linearization to constrained optimization--derive convergence rates, uncover connections to Sequential Quadratic Programming, and introduce a momentum-accelerated variant for faster convergence

Abstract:

Constrained optimization is fundamental to numerous applications. While first-order iterative algorithms are widely used for solving these problems, understanding their continuous-time counterparts—formulated as differential equations—can provide valuable theoretical insights into stability and convergence. Among various approaches, Feedback Linearization (FL), a well-established nonlinear control technique, has demonstrated potential for addressing nonconvex equality-constrained optimization problems, yet remains relatively underexplored.

This paper aims to develop rigorous theoretical foundations for applying feedback linearization to solve constrained optimization. For equality-constrained optimization, we establish global convergence rates to first-order Karush-Kuhn-Tucker (KKT) points and uncover the close connection between the FL method and the Sequential Quadratic Programming (SQP) algorithm. Building on this relationship, we extend the FL approach to handle inequality-constrained problems. Furthermore, we introduce a momentum-accelerated FL algorithm that achieves faster convergence, and provide a rigorous convergence guarantee.

Primary Area: Optimization

Keywords: Constrained Optimization, Control Perspective for Optimization, Feedback Linearization

Submission Number: 14487