An error bound estimation for the positive semi-definite tensor complementarity problem and its applications

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.