What question did this study set out to answer?

The research aims to address optimization problems on the Stiefel manifold using a novel gradient method.

March 19, 2026Open Access

An Intrinsic Scaled Riemannian Nonmonotone Conjugate Gradient Method on Stiefel Manifold

Puntos clave

The research aims to address optimization problems on the Stiefel manifold using a novel gradient method.
Proposed a new intrinsic vector transport based on QR-type retraction.
Developed an intrinsic Riemannian nonmonotone conjugate gradient method.
Established global convergence for the intrinsic scaled version of this method.
Numerical results demonstrate the method's effectiveness on a range of optimization challenges.
The proposed method shows superior performance compared to existing techniques.

Resumen

In this paper, we focus on the optimization problem on the Stiefel manifold. Based on the inverse process of the QR-type retraction, we propose a new intrinsic vector transport. In combination with Dai’s nonmonotone conjugate gradient (CG) method, we present an intrinsic Riemannian nonmonotone CG method and its scaled version and establish the global convergence of the intrinsic scaled Riemannian nonmonotone CG method. Numerical results on a variety of optimization problems on Stiefel manifolds indicate the effectiveness of the proposed method.

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