Rank-one approximation of a higher-order tensor by a Riemannian trust-region method

Jianheng Chen () and Wen Huang ()
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Jianheng Chen: Zhejiang University of Water Resources and Electric Power
Wen Huang: Xiamen University

Computational Optimization and Applications, 2025, vol. 90, issue 2, No 7, 515-556

Abstract: 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.

Keywords: Higher-order tensor; Rank-one approximation; Riemannian Hessian; Trust-region method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00634-z

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