A Modulus-Based Formulation for the Vertical Tensor Complementarity Problem

In this paper, we introduce a modulus-based formulation for solving vertical tensor complementarity problems (VTCP) with an arbitrary number of tensors. This formulation allows us to design the modulus-based tensor splitting iterative method to fit different number of tensors. In this context, we especially analyze the modulus-based tensor splitting iterative methods for solving VTCP with two tensors, and provide sufficient conditions in combination with the properties of the power Lipschitz tensor for their convergence. We then extend the methods to solve VTCP with any number of tensors, and study the convergence analysis under proper conditions. Finally, the proposed methods are evaluated by numerical experiments.