Riemannian interior point methods achieve local near-quadratic convergence to second-order stationary points, with the first algorithm shown to combine this local rate and global convergence guarantees.
Mathematical Programming 89(1), 149–185 (2000) 38 Mitsuaki Obara, Takayuki Okuno, and Akiko Takeda
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Local near-quadratic convergence of Riemannian interior point methods
Riemannian interior point methods achieve local near-quadratic convergence to second-order stationary points, with the first algorithm shown to combine this local rate and global convergence guarantees.