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On global convergence of alternating least squares for tensor approximation

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  • Yuning Yang

    (Guangxi University)

Abstract

Alternating least squares is a classic, easily implemented, yet widely used method for tensor canonical polyadic approximation. Its subsequential and global convergence is ensured if the partial Hessians of the blocks during the whole sequence are uniformly positive definite. This paper shows that this positive definiteness assumption can be weakened in two ways. Firstly, if the smallest positive eigenvalues of the partial Hessians are uniformly positive, and the solutions of the subproblems are properly chosen, then global convergence holds. This allows the partial Hessians to be only positive semidefinite. Next, if at a limit point, the partial Hessians are positive definite, then global convergence also holds. We also discuss the connection of such an assumption to the uniqueness of exact CP decomposition.

Suggested Citation

  • Yuning Yang, 2023. "On global convergence of alternating least squares for tensor approximation," Computational Optimization and Applications, Springer, vol. 84(2), pages 509-529, March.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:2:d:10.1007_s10589-022-00428-1
    DOI: 10.1007/s10589-022-00428-1
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    References listed on IDEAS

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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. Laurent Sorber & Ignat Domanov & Marc Barel & Lieven Lathauwer, 2016. "Exact line and plane search for tensor optimization," Computational Optimization and Applications, Springer, vol. 63(1), pages 121-142, January.
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