The paper proposes an inexact adaptive cubic regularization algorithm for solving large-scale separable unconstrained optimization problems on general Riemannian manifolds. The key highlights are:
The algorithm employs the inexact gradient and Hessian information, which is particularly useful in large-scale settings where the exact gradient and Hessian computations can be expensive.
The algorithm is proven to have an iteration complexity of O(max{ε^-2_g, ε^-3_H}) for achieving the (ε_g, ε_H)-optimality under certain assumptions on the accuracies of the inexact gradient and Hessian.
The paper also establishes the iteration complexities of the deterministic Riemannian adaptive cubic regularization algorithm and the inexact Riemannian adaptive cubic regularization algorithm under the true gradient.
As an application, the proposed algorithms are applied to solve the joint diagonalization problem on the Stiefel manifold. Numerical experiments show that the inexact algorithms outperform the deterministic algorithm and the inexact trust-region algorithm.
To Another Language
from source content
arxiv.org
Key Insights Distilled From
by Z. Y. Li,X. ... at arxiv.org 05-07-2024
https://arxiv.org/pdf/2405.02588.pdfDeeper Inquiries