An Improved Riemannian Trust-Region Method Combining Line Search Techniques with Applications in Matrix Optimization
Year: 2026
Type: article
Abstract: We propose a hybrid Riemannian optimization framework that combines trust-region methods with retraction-based backtracking line search to reduce the cost of repeatedly solving subproblems corresponding to rejected trial steps. If a trust-region step is not accepted, the algorithm reuses the descent direction and performs a backtracking line search instead of resolving the subproblem. Under the stated assumptions, we establish lim infk→∞∥gradf(xk)∥xk=0. Numerical experiments on three matrix optimization problems with orthogonality constraints, namely Brockett cost function minimization on the Stiefel manifold, Rayleigh quotient minimization on the sphere manifold, and independent component analysis on the Stiefel manifold, demonstrate that RTR-LS and LRTR-LS are computationally more efficient than classical Riemannian trust-region methods.
Source: Mathematics
DOI: 10.3390/math14214098
Authors: Jiahui Yuan, Tao Yan
Institution: Nanjing University of Science and Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7225645024
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