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February 3, 2026Applied Numerical Mathematics

A class of generalized Barzilai-Borwein methods for Riemannian optimization

Shajie Xing Huangyue Chen Chunming Tang

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Key Points

These generalized Barzilai-Borwein methods enable faster convergence in Riemannian optimization, improving efficiency overall.
With improved convergence rates, these methods facilitate optimization problems in complex geometrical spaces, particularly in machine learning applications.
The analysis utilizes gradient descent techniques on Riemannian manifolds, enhancing traditional optimization frameworks significantly.
The implications suggest broad applications in advanced machine learning and optimization fields, highlighting a need for future exploratory work.

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Implication

Demonstrates new Barzilai-Borwein methods improve convergence rates in Riemannian optimization, suggesting enhanced efficiency for complex problems.

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Cite This Study

Xing et al. (2026) studied this question.

synapsesocial.com/papers/69a760bec6e9836116a2dc82 https://doi.org/10.1016/j.apnum.2026.01.019

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Keep reading

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1A Brief Introduction to Manifold OptimizationOriginal Research · 2020 · 193 citations
2Two-Point Step Size Gradient MethodsOriginal Research · 1988 · 2,877 citations
3On the Barzilai and Borwein choice of steplength for the gradient methodOriginal Research · 1993 · 397 citations
4R-linear convergence of the Barzilai and Borwein gradient methodOriginal Research · 2002 · 308 citations
5The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization ProblemOriginal Research · 1997 · 791 citations

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