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<p>In this paper, we focus on the low Tucker rank tensor completion problem. We reformulate it as a multilinear group sparse optimization problem equivalently. For the reformulated problem, we design an alternating linearized proximal algorithm to solve it. Based on the Kurdyka-Łojasiewicz (KL) property, the convergence theory and convergence rate of the proposed algorithm are analyzed. Finally, extensive numerical experiments validate the effectiveness of our proposed algorithm.</p>

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Alternating Linearized Proximal Algorithm for the Low Tucker Rank Tensor Completion Problem

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Xinzhen Zhang,
  • Xueyou Wang,
  • Wendong Si

摘要

In this paper, we focus on the low Tucker rank tensor completion problem. We reformulate it as a multilinear group sparse optimization problem equivalently. For the reformulated problem, we design an alternating linearized proximal algorithm to solve it. Based on the Kurdyka-Łojasiewicz (KL) property, the convergence theory and convergence rate of the proposed algorithm are analyzed. Finally, extensive numerical experiments validate the effectiveness of our proposed algorithm.