A sparse optimization approach for simultaneous orthogonal tensor diagonalization

Xinying Li, Chao Chang, Jianze Li and Yuning Yang

Applied Mathematics and Computation, 2025, vol. 490, issue C

Abstract: This paper presents a sparse optimization method for the simultaneous orthogonal tensor diagonalization. The model treats off-diagonal elements of tensors as entities requiring sparsity, guided by an ℓ1 norm regularizer to optimize the diagonalization process. A gradient-based alternating multi-block Jacobi-AMB algorithm is developed to address the optimization problem on the product of orthogonal groups. We establish the global convergence based on the Kurdyka-Łojasiewicz property. Numerical experiments demonstrate that the Jacobi-AMB performs well in efficiency; under certain circumstances, its stability and effectiveness also perform well.

Keywords: Sparse optimization; Simultaneous diagonalization; Jacobi-type algorithm; Global convergence; Kurdyka-Łojasiewicz property (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006647

DOI: 10.1016/j.amc.2024.129203

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