Riemannian Trust Region Methods for SC 1 Minimization
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10915_2024_2664_ReferencePDF.pdf
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Author(s)
Zhang, Chenyu
Xiao, Rufeng
Huang, Wen
Jiang, Rujun
Date Issued
September 20, 2024
Journal
Journal of Scientific Computing
Publisher
Springer US
Citation
Zhang, C., Xiao, R., Huang, W. et al. Riemannian Trust Region Methods for Minimization. J Sci Comput 101, 32 (2024).
Version
Author's final manuscript
Abstract
Manifold optimization has recently gained significant attention due to its wide range of applications in various areas. This paper introduces the first Riemannian trust region method for minimizing an SC 1 function, which is a differentiable function that has a semismooth gradient vector field, on manifolds with convergence guarantee. We provide proof of both global and local convergence results, along with demonstrating the local superlinear convergence rate of our proposed method. As an application and to demonstrate our motivation, we utilize our trust region method as a subproblem solver within an augmented Lagrangian method for minimizing nonsmooth nonconvex functions over manifolds. This represents the first approach that fully explores the second-order information of the subproblem in the context of augmented Lagrangian methods on manifolds. Numerical experiments confirm that our method outperforms existing methods.
MIT Department
MIT Institute for Data, Systems, and Society
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10915-024-02664-5
