An Fixed Point Iterative Method for Tensor Complementarity Problems

Nonlinear fixed point iterative method for finding a solution of the tensor complementarity problem (TCP) are proposed in this paper. Theoretical analysis shows that tensor complementarity problems are equivalent to a fixed point equation with monotonic increasing odd function. A fixed point iterative method is proposed based on the fixed point equation, and corresponding convergence results are studied. The computer-simulation results further substantiate that the proposed fixed point iterative method can find a solution of the TCP.

Automated summary

This paper proposes a nonlinear fixed point iterative method for finding a solution of the tensor complementarity problem (TCP). Theoretical analysis shows that tensor complementarity problems can be represented as a fixed point equation with a monotonic increasing odd function. A fixed point iterative method is proposed based on this equation, and the convergence results are studied. Computer-simulation results further validate the effectiveness of the proposed method in solving the TCP.