Novel Product Manifold Modeling and Orthogonality-Constrained Neural Network Solver for Parameterized Generalized Inverse Eigenvalue Problems
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908786560598016 |
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| author | Zhang, Shuai Jiang, Xuelian Xu, Yingxiang |
| author_facet | Zhang, Shuai Jiang, Xuelian Xu, Yingxiang |
| contents | A parameterized orthogonality-constrained neural network is proposed for the first time to solve the parameterized generalized inverse eigenvalue problem (PGIEP) on product manifolds, offering a new perspective to address PGIEP. The key contributions are twofold. First, we construct a novel model for the PGIEP, where the optimization variables are located on the product of a Stiefel manifold and a Euclidean manifold. This model enables the application of optimization algorithms on the Stiefel manifold, a capability that is not achievable with existing models. Additionally, the gradient Lipschitz continuity of the objective function is proved. Second, a parameterized Stiefel multilayer perceptron (P-SMLP) that incorporates orthogonality constraints is proposed. Through hard constraints, P-SMLP enables end-to-end training without the need of alternating training between the two manifolds, providing a robust computational framework for generic PGIEPs. Numerical experiments demonstrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Novel Product Manifold Modeling and Orthogonality-Constrained Neural Network Solver for Parameterized Generalized Inverse Eigenvalue Problems Zhang, Shuai Jiang, Xuelian Xu, Yingxiang Numerical Analysis A parameterized orthogonality-constrained neural network is proposed for the first time to solve the parameterized generalized inverse eigenvalue problem (PGIEP) on product manifolds, offering a new perspective to address PGIEP. The key contributions are twofold. First, we construct a novel model for the PGIEP, where the optimization variables are located on the product of a Stiefel manifold and a Euclidean manifold. This model enables the application of optimization algorithms on the Stiefel manifold, a capability that is not achievable with existing models. Additionally, the gradient Lipschitz continuity of the objective function is proved. Second, a parameterized Stiefel multilayer perceptron (P-SMLP) that incorporates orthogonality constraints is proposed. Through hard constraints, P-SMLP enables end-to-end training without the need of alternating training between the two manifolds, providing a robust computational framework for generic PGIEPs. Numerical experiments demonstrate the effectiveness of the proposed method. |
| title | Novel Product Manifold Modeling and Orthogonality-Constrained Neural Network Solver for Parameterized Generalized Inverse Eigenvalue Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.17798 |