Modified Armijo line search in optimization on Riemannian submanifolds with reduced computational cost

Hiroyuki Sato, Yuya Yamakawa and Kensuke Aihara

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 245, issue C, 260-274

Abstract: For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing methods need to compute the value of a retraction mapping regarding the search direction several times at each iteration; this may result in high computational costs, particularly if computing the value of the retraction is expensive. To address this issue, this study focuses on embedded Riemannian submanifolds of the Euclidean spaces and proposes a novel Riemannian line search that achieves lower computational cost by incorporating a new strategy that computes the retraction only when inevitable. A class of Riemannian optimization algorithms, including the steepest descent and Newton methods, with the new line search strategy is proposed and proved to be globally convergent. Furthermore, numerical experiments on solving optimization problems on several types of embedded Riemannian submanifolds illustrate that the proposed methods are superior to the standard Riemannian Armijo line search-based methods.

Keywords: Riemannian optimization; Steepest descent method; Newton method; Armijo line search; Low computational cost; Global convergence (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475426000030
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:245:y:2026:i:c:p:260-274

DOI: 10.1016/j.matcom.2026.01.003

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().