A Safeguarded Transport-Extrapolated Proximal Gradient Method on the Stiefel Manifold
- 1School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
- 2National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing 401331, China
Abstract
Motivated by sparse principal component analysis (PCA), this paper proposes ATE-ManPG, a safeguarded transport-extrapolated proximal gradient method for minimizing the sum of a smooth function and a convex, possibly nonsmooth function over the Stiefel manifold. The method augments the manifold proximal gradient method (ManPG) with two ingredients: momentum obtained by transporting the previous proximal search direction to the current tangent space, protected by a monotone restart safeguard, and a bounded adaptive proximal parameter. For the exact idealized iteration, global convergence to stationary points and O(1/ε2) iteration complexity are proved; under a proximal Kurdyka–Łojasiewicz condition with exponent 1/2 and a relative-error condition, both stated as explicit hypotheses, the convergence is R-linear. Experiments on a sparse-PCA model, validated by an external residual certificate at the returned point, show a 3.6× mean iteration-count reduction relative to fixed-parameter ManPG; a factorial ablation attributes most of this reduction to the adaptive parameter, while transported momentum adds a further 6.4% on average, concentrated in one paired trial.
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BibTeX
@article{yan2026safeguarded,
title = {{A Safeguarded Transport-Extrapolated Proximal Gradient Method on the Stiefel Manifold}},
author = {Chuanjun Yan and Lin Chen},
journal = {Axioms},
year = {2026},
month = nov,
doi = {10.3390/axioms15110828},
url = {https://www.mdpi.com/2075-1680/15/11/828},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Safeguarded Transport-Extrapolated Proximal Gradient Method on the Stiefel Manifold
AU - Chuanjun Yan
AU - Lin Chen
PY - 2026
DA - 2026/11/05
JO - Axioms
DO - 10.3390/axioms15110828
UR - https://www.mdpi.com/2075-1680/15/11/828
AB - Motivated by sparse principal component analysis (PCA), this paper proposes ATE-ManPG, a safeguarded transport-extrapolated proximal gradient method for minimizing the sum of a smooth function and a convex, possibly nonsmooth function over the Stiefel manifold. The method augments the manifold proximal gradient method (ManPG) with two ingredients: momentum obtained by transporting the previous proximal search direction to the current tangent space, protected by a monotone restart safeguard, and a bounded adaptive proximal parameter. For the exact idealized iteration, global convergence to stationary points and O(1/ε2) iteration complexity are proved; under a proximal Kurdyka–Łojasiewicz condition with exponent 1/2 and a relative-error condition, both stated as explicit hypotheses, the convergence is R-linear. Experiments on a sparse-PCA model, validated by an external residual certificate at the returned point, show a 3.6× mean iteration-count reduction relative to fixed-parameter ManPG; a factorial ablation attributes most of this reduction to the adaptive parameter, while transported momentum adds a further 6.4% on average, concentrated in one paired trial.
SN - 2075-1680
ER -