Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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GLOBAL CONVERGENCE OF A BARZILAI-BORWEIN SCALING HZ-TYPE RIEMANNIAN CONJUGATE GRADIENT METHOD

  • ZIYIN MA (Department of Mathematics, School of Mathematics and Statistics, Nanjing University of Science and Technology) ;
  • TAO YAN (Department of Computational Mathematics, School of Mathematics and Statistics, Nanjing University of Science and Technology) ;
  • SHIMIN ZHAO (Department of Mathematics and Information Science, Yantai University)
  • Received : 2025.07.09
  • Accepted : 2026.03.16
  • Published : 2026.05.30
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Abstract

We propose an improved Riemannian conjugate gradient method with Barzilai-Borwein scaling (BBSRCG) for unconstrained manifold optimization, which extends the HZ-RCG framework through BB method while preserving sufficient descent properties regardless of whether a line search is used or not. Under mild assumptions, we establish the global convergence for u-strongly geodesically convex functions on Riemannian manifolds. Numerical experiments show the improved performance over existing Riemannian conjugate gradient methods on both synthetic and real-world datasets.

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Acknowledgement

The author would like to thank the referees for useful comments and suggestions that improved the paper.

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