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<p>In this paper, we propose a new Riemannian optimization algorithm that leverages information from previous search directions. Generally, such algorithms are referred to as memory gradient methods, which have proven highly effective in unconstrained optimization. However, none of these methods have yet been extended to the Riemannian setting. In this study, we extend the memory gradient method for optimization on manifolds and investigate the necessary conditions for its convergence to first-order critical points. A notable advantage of our approach is that it does not depend on any assumptions regarding the impact of vector transport on the norm of the search direction. Finally, we conduct numerical experiments to evaluate the performance of the proposed method.</p>

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A Globally Convergent Riemannian Memory Gradient Method

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • Shahabeddin Najafi,
  • Masoud Hajarian

摘要

In this paper, we propose a new Riemannian optimization algorithm that leverages information from previous search directions. Generally, such algorithms are referred to as memory gradient methods, which have proven highly effective in unconstrained optimization. However, none of these methods have yet been extended to the Riemannian setting. In this study, we extend the memory gradient method for optimization on manifolds and investigate the necessary conditions for its convergence to first-order critical points. A notable advantage of our approach is that it does not depend on any assumptions regarding the impact of vector transport on the norm of the search direction. Finally, we conduct numerical experiments to evaluate the performance of the proposed method.