黎曼流形上的子采样自适应信任区域法

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2024-04-13 DOI:10.1002/nla.2557

Shimin Zhao, Tao Yan, Yuanguo Zhu

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引用次数: 0

摘要

我们考虑了黎曼流形上的大规模有限和最小化问题。我们在黎曼流形上开发了一种子采样自适应信任区域方法。基于非精确信息，我们采用自适应技术灵活调整方法中的信任区域半径。我们提出了算法达到二阶静止点时的迭代复杂度，这与信任区域方法的结果相吻合。报告了格拉斯曼流形上 PCA 和低秩矩阵补全的数值结果，以证明所提出的黎曼方法的有效性。

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Sub‐sampled adaptive trust region method on Riemannian manifolds

We consider the problem of large‐scale finite‐sum minimization on Riemannian manifold. We develop a sub‐sampled adaptive trust region method on Riemannian manifolds. Based on inexact information, we adopt adaptive techniques to flexibly adjust the trust region radius in our method. We present the iteration complexity is when the algorithm attains an ‐second‐order stationary point, which matches the result on trust region method. Numerical results for PCA on Grassmann manifold and low‐rank matrix completion are reported to demonstrate the effectiveness of the proposed Riemannian method.

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.