The Vertical Tensor Complementarity Problem via Two Randomized Algorithms

In this paper, inspired by this work [Wang, X, M Che and Y Wei (2022a). Randomized Kaczmarz methods for tensor complementarity problems. Computational Optimization and Applications, 82(3), 595–615], we consider two randomized algorithms, i.e., the modified randomized Kaczmarz (MRK) algorithm and the modified randomized coordinate descent (MRCD) algorithm, to solve the vertical tensor complementarity problem of type strong EVP tensor, by reformulating it into an equivalent fixed point equation. We further derive the upper bound of the mean squared error and estimate of convergence rate for MRK and MRCD algorithms. Some examples are presented to show the feasibility and effectiveness of the proposed methods.