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<p>In this article, we propose two structured Riemannian spectral conjugate gradient methods that incorporate retraction and scaled vector transport operators. These methods ensure sufficient descent properties regardless of the line search strategy employed. We establish their global convergence under nonexpansive and Lipschitz-type continuity conditions. Utilizing the Pymanopt package, we evaluate the performance of the proposed methods on seven practical optimization problems defined on manifolds. The performance analysis, based on well-known benchmarking measures in global optimization, involves 200 independent experimental instances. The proposed methods demonstrate promising results compared to a previously introduced spectral Riemannian conjugate gradient method and other established Riemannian optimization approaches, including RFR and MRFR.</p>

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On New Spectral Conjugate Gradient Methods for Riemannian Optimization Using Retraction and Scaled Vector Transport

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • Nasiru Salihu,
  • Poom Kumam,
  • Sani Salisu,
  • Kanokwan Sitthithakerngkiet

摘要

In this article, we propose two structured Riemannian spectral conjugate gradient methods that incorporate retraction and scaled vector transport operators. These methods ensure sufficient descent properties regardless of the line search strategy employed. We establish their global convergence under nonexpansive and Lipschitz-type continuity conditions. Utilizing the Pymanopt package, we evaluate the performance of the proposed methods on seven practical optimization problems defined on manifolds. The performance analysis, based on well-known benchmarking measures in global optimization, involves 200 independent experimental instances. The proposed methods demonstrate promising results compared to a previously introduced spectral Riemannian conjugate gradient method and other established Riemannian optimization approaches, including RFR and MRFR.