Constrained Optimization From a Control Perspective via Feedback Linearization

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

Keywords: Constrained Optimization; Control Theory; Feedback Linearization

TL;DR: This paper develops a feedback linearization framework for constrained optimization, with convergence guarantees, a connection to SQP, and a momentum-accelerated variant.

Abstract: Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization—a well-established nonlinear control technique—to solve constrained optimization problems. 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 feedback linearization algorithm and provide a rigorous convergence guarantee.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 13065