<p>This paper introduces an adaptive restart Riemannian spectral conjugate gradient method for solving unconstrained optimization problems on Riemannian manifolds. Motivated by the efficient Dai-Kou conjugate parameter in Euclidean space, we extend it to the Riemannian setting and combine it with a Riemannian quasi-Newton method to derive a bounded spectral parameter via a double truncation technique. An adaptive restart strategy is integrated into the search direction to ensure sufficient descent without a line search and to enhance numerical performance. Under the strong Wolfe line search conditions, the global convergence of the proposed method is established. Numerical experiments on Riemannian optimization problems demonstrate the efficiency of our method compared with several existing Riemannian conjugate gradient algorithms.</p>

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An adaptive restart Riemannian spectral Dai-Kou conjugate gradient method with quasi-Newton update

  • Yun Wang,
  • Hu Shao,
  • Huayu Sun,
  • Ting Wu

摘要

This paper introduces an adaptive restart Riemannian spectral conjugate gradient method for solving unconstrained optimization problems on Riemannian manifolds. Motivated by the efficient Dai-Kou conjugate parameter in Euclidean space, we extend it to the Riemannian setting and combine it with a Riemannian quasi-Newton method to derive a bounded spectral parameter via a double truncation technique. An adaptive restart strategy is integrated into the search direction to ensure sufficient descent without a line search and to enhance numerical performance. Under the strong Wolfe line search conditions, the global convergence of the proposed method is established. Numerical experiments on Riemannian optimization problems demonstrate the efficiency of our method compared with several existing Riemannian conjugate gradient algorithms.