Global convergence of Riemannian line search methods with a Zhang-Hager-type condition

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In this paper, we analyze the global convergence of a general non-monotone line search method on Riemannian manifolds. For this end, we introduce some properties for the tangent search directions that guarantee the convergence, to a stationary point, of this family of optimization methods under appropriate assumptions. A modified version of the non-monotone line search of Zhang and Hager is the chosen globalization strategy to determine the step-size at each iteration. In addition, we develop a new globally convergent Riemannian conjugate gradient method that satisfies the direction assumptions introduced in this work. Finally, some numerical experiments are performed in order to demonstrate the effectiveness of the new procedure.

Original languageEnglish
Pages (from-to)1183-1203
Number of pages21
JournalNumerical Algorithms
Issue number3
StatePublished - Nov 2022
Externally publishedYes


  • Descent method
  • Global convergence
  • Inexact line search
  • Non-monotone line search
  • Riemannian manifolds


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