@article{Zhang2025, 
author = {Yuanshou Zhang and Hongchun Sun and Zhiwen Jie and Sabir Amina},
title = {An error bound estimation for the positive semi-definite tensor complementarity problem and its applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20805-20824},
keywords = {positive semi-definite TCP, error bound, self-adaptive projection algorithm, global R-linear convergence rate},
url = {https://www.sciopen.com/article/10.3934/math.2025929},
doi = {10.3934/math.2025929},
abstract = {For the positive semi-definite tensor complementarity problem (TCP), based on the natural residual function, we first established an error bound estimation for the positive semi-definite TCP without the fractional term of the residual function. Compared with the existing results, the requirements imposed on the TCP such as being an    m-uniform    P-function and being    m-monotone were removed. As an application of the error bound obtained, we showed the global    R-linear convergence rate of the proposed self-adaptive projection algorithm for solving the TCP via an equivalent transformation of this problem. Meanwhile, we also obtained an    ϵ-optimal solution in a finite number of iterations. Finally, numerical results were reported to demonstrate the efficiency of the proposed method.}
}