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<p>In this paper, we investigate the global uniqueness and solvability for the third-order tensor linear complementarity problems. Furthermore, we transform equivalently this type of complementarity problems into the modulus equations and then we establish the modulus-based nonsmooth Newton’s method and the modulus-based tensor splitting method. Besides, we also give a mixed algorithm for finding an initial tensor. Numerical examples including both the synthetic data and the real data from grayscale images deblurring are given to demonstrate the efficiency of the proposed algorithms.</p>

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Solving third-order tensor linear complementarity problems via modulus-based methods and applications

  • 期刊论文

  • 发表日期：

    2025年2月24日

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  • Ting Hu,
  • Dongdong Liu,
  • Seak-Weng Vong

摘要

In this paper, we investigate the global uniqueness and solvability for the third-order tensor linear complementarity problems. Furthermore, we transform equivalently this type of complementarity problems into the modulus equations and then we establish the modulus-based nonsmooth Newton’s method and the modulus-based tensor splitting method. Besides, we also give a mixed algorithm for finding an initial tensor. Numerical examples including both the synthetic data and the real data from grayscale images deblurring are given to demonstrate the efficiency of the proposed algorithms.