A modulus-based formulation for the vertical linear complementarity problem

We introduce a modulus-based formulation for vertical linear complementarity problems (VLCPs) with an arbitrary number l of matrices. This formulation can be used to set up a variety of modulus-based solution methods, including, for example, the modulus-based matrix splitting methods for VLCPs that we here introduce. In this context, we particularly analyze the methods for problems with l = 2 (providing also sufficient conditions for their global convergence) and we then generalize the formulation of the methods to any l. Finally, some numerical experiments are solved to evaluate the performance of the proposed methods, which we compare with an existing smoothing Newton method for VLCPs.