The paper introduces a novel approach to optimization problems on Riemannian manifolds using memoryless quasi-Newton methods. It compares various methods, including the proposed algorithm, with numerical experiments showcasing superior performance under different parameter settings.
The study delves into the theoretical foundations of Riemannian optimization and proposes an innovative algorithm based on the spectral-scaling Broyden family. By leveraging concepts like retraction and vector transport, the method aims to optimize off-diagonal cost functions efficiently.
Key highlights include the formulation of search directions satisfying sufficient descent conditions, global convergence analyses under specific conditions, and comparisons with existing algorithms. The research emphasizes practical applications in solving complex optimization problems on manifolds.
Overall, the paper contributes valuable insights into memoryless quasi-Newton methods tailored for Riemannian optimization challenges. It underscores the significance of parameter selection and algorithm design in achieving optimal convergence rates and computational efficiency.
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by Hiroyuki Sak... at arxiv.org 03-11-2024
https://arxiv.org/pdf/2307.08986.pdfDeeper Inquiries