Constrained Optimization From a Control Perspective via Feedback Linearization

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 (FL) – 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.

💡 Research Summary

This paper establishes a rigorous control‑theoretic foundation for solving constrained optimization problems using feedback linearization (FL), a classical technique from nonlinear control. The authors first reformulate equality‑constrained optimization as a control system in which the decision variable (x) is the state and the Lagrange multiplier (\lambda) serves as the control input. The continuous‑time dynamics are defined as (\dot x = -T(x)(\nabla f(x) + J_h(x)^\top \lambda)), where (T(x)) is a positive‑definite matrix and (J_h(x)) is the Jacobian of the equality constraints (h(x)=0). By choosing the control law (\lambda = -