Randomized Kaczmarz methods for tensor complementarity problems

Xuezhong Wang, Maolin Che, Yimin Wei

Abstract: In this paper, we equivalently reformulate the tensor complementarity problem as a system of fixed point equations. Based on this system, we propose the (extend) randomized Kaczmarz methods for solving the tensor complementarity problem associated with nonnegative \(\mathcal {P}\)-tensors and nonsingular \(\mathcal {M}\)-tensors. We also analyze the upper bounds of the mean squared error and the estimate of the convergence rate for these two iterative methods. The computer simulation results further substantiate that the presented two randomized Kaczmarz type methods can be used to solve TCP with these two cases of tensors.