An Accelerated Riemannian Conjugate Gradient Method Based on the Barzilai–Borwein Technique

This paper proposes an accelerated Riemannian conjugate gradient method based on the Barzilai-Borwein (BB) technique, termed ABBSRCG, for unconstrained optimization on Riemannian manifolds. Building upon classical Riemannian conjugate gradient frameworks, the method enhances step-size selection through a Wolfe-condition-informed strategy and incorporates a dynamic mechanism that adaptively adjusts the computed step length. The resulting algorithm achieves both high efficiency and numerical stability. Compared to conventional approaches such as the Fletcher-Reeves (FR)- type Riemannian conjugate gradient method, the Dai-Yuan (DY)- type Riemannian conjugate gradient method, ABBSRCG maintains the sufficient descent property regardless of whether a line search is used or not. Under mild assumptions, we establish the global convergence of ABBSRCG for u-strongly geodesically convex functions on Riemannian manifolds. Experiments on sphere and oblique manifolds show that ABBSRCG requires fewer iterations and achieves higher computational efficiency than existing Riemannian conjugate gradient methods, confirming its efficiency and reliability for large-scale Riemannian optimization problems.