A Globally Convergent Riemannian Memory Gradient Method

Shahabeddin Najafi () and Masoud Hajarian ()
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Shahabeddin Najafi: Faculty of Mathematical Sciences, Shahid Beheshti University
Masoud Hajarian: Faculty of Mathematical Sciences, Shahid Beheshti University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 32, 17 pages

Abstract: Abstract 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.

Keywords: Memory gradient method; Riemannian manifolds; Geometric optimization; Line search method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02736-y

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