Analysis of Sequential Quadratic Programming through the Lens of Riemannian Optimization.

We prove that a first-order Sequential Quadratic Programming (SQP) algorithm for equality constrained optimization has local linear convergence with rate $(1-1/kappa_R)^k$, where $kappa_R$ is the condition number of the Riemannian Hessian, and global convergence with rate $k^{-1/4}$. Our analysis builds on insights from Riemannian optimization -- we show that the SQP and Riemannian gradient methods have nearly identical behavior near the constraint manifold, which could be of broader interest for understanding constrained optimization.