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.