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arXiv · 1805.08756

Analysis of Sequential Quadratic Programming through the Lens of Riemannian Optimization

Yu Bai·Song Mei
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Abstract

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.

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Yu Bai, Song Mei. 2018-05-22. Analysis of Sequential Quadratic Programming through the Lens of Riemannian Optimization. https://arxiv.org/abs/1805.08756

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