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<p>In 2006, the first spectral Fletcher–Reeves conjugate gradient (CG) parameter was introduced, accompanied by a convergence analysis based on the exact line search procedure. To avoid the need for an exact line search, this paper introduces a generalized spectral CG parameter based on a revised Fletcher–Reeves spectral (rFRS) approach in Riemannian optimization. The proposed parameter ensures the sufficient descent property without requiring a line search. Global convergence is demonstrated under mild assumptions. Numerical experiments show that the proposed scheme outperforms existing Riemannian CG methods in terms of efficiency. It also demonstrates robust performance across five different Riemannian optimization problems. Furthermore, the rFRS method demonstrates efficient results in solving inverse problems associated with the Gough–Stewart platform.</p>

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Spectral conjugate gradient for Riemannian optimization: application to the Gough–Stewart platform

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • Salihu Nasiru,
  • Poom Kumam,
  • Sani Salisu,
  • Lin Wang,
  • Thidaporn Seangwattana

摘要

In 2006, the first spectral Fletcher–Reeves conjugate gradient (CG) parameter was introduced, accompanied by a convergence analysis based on the exact line search procedure. To avoid the need for an exact line search, this paper introduces a generalized spectral CG parameter based on a revised Fletcher–Reeves spectral (rFRS) approach in Riemannian optimization. The proposed parameter ensures the sufficient descent property without requiring a line search. Global convergence is demonstrated under mild assumptions. Numerical experiments show that the proposed scheme outperforms existing Riemannian CG methods in terms of efficiency. It also demonstrates robust performance across five different Riemannian optimization problems. Furthermore, the rFRS method demonstrates efficient results in solving inverse problems associated with the Gough–Stewart platform.