Rank-one approximation of a higher-order tensor by a Riemannian trust-region method: Rank-one approximation of a higher-order tensor by a Riemannian...: J. Chen, W. Huang.
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| Title: | Rank-one approximation of a higher-order tensor by a Riemannian trust-region method: Rank-one approximation of a higher-order tensor by a Riemannian...: J. Chen, W. Huang. |
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| Authors: | Chen, Jianheng1,2 (AUTHOR) cjh868@126.com, Huang, Wen2 (AUTHOR) wen.huang@xmu.edu.cn |
| Source: | Computational Optimization & Applications. Mar2025, Vol. 90 Issue 2, p515-556. 42p. |
| Subjects: | Computational mathematics, Tangent function, Vector valued functions |
| Abstract: | In this paper, we consider a rank-one approximation problem of a higher-order tensor. We treat the problem as an optimization model on a Cartesian product of manifolds and solve this model by using a Riemannian optimization method. We derive the action of the Riemannian Hessian of the objective function on tangent vectors to the Cartesian product of manifolds. A Riemannian trust-region method with block-diagonal Hessian is used to solve this model, and the subproblem is solved by the truncated conjugate gradient method. The convergence analysis of the Riemannian trust-region method has been established in the literature with certain assumptions. We verify those assumptions for the rank-one approximation problem. Numerical experiments illustrate that the proposed model with the method is feasible and effective. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | In this paper, we consider a rank-one approximation problem of a higher-order tensor. We treat the problem as an optimization model on a Cartesian product of manifolds and solve this model by using a Riemannian optimization method. We derive the action of the Riemannian Hessian of the objective function on tangent vectors to the Cartesian product of manifolds. A Riemannian trust-region method with block-diagonal Hessian is used to solve this model, and the subproblem is solved by the truncated conjugate gradient method. The convergence analysis of the Riemannian trust-region method has been established in the literature with certain assumptions. We verify those assumptions for the rank-one approximation problem. Numerical experiments illustrate that the proposed model with the method is feasible and effective. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 09266003 |
| DOI: | 10.1007/s10589-024-00634-z |
