Modified Armijo line-search in Riemannian optimization with reduced computational cost

In this paper, we propose a new line-search method that improves the ordinary Armijo line-search in Riemannian optimization. For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Armijo line-search in...

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Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Yamakawa, Yuya, Sato, Hiroyuki, Aihara, Kensuke
Format: Article
Language:English
Subjects:
Algorithms
Computational efficiency
Computing costs
Convergence
Iterative methods
Newton methods
Optimization
Riemann manifold
Search methods
Online Access:Get full text
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Summary:In this paper, we propose a new line-search method that improves the ordinary Armijo line-search in Riemannian optimization. For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Armijo line-search in Riemannian optimization for global convergence. Such existing methods need the computation of a retraction regarding the search direction for each iteration. On the other hand, the proposed line-search decreases the computational cost by incorporating a new strategy that computes the retraction only if a promising candidate for the step length is found. We further present a Riemannian Newton method with the new line-search strategy and prove its global convergence.
ISSN:2331-8422