On the equivalence between some projected and modulus-based splitting methods for linear complementarity problems

In this paper, we analyze the relationship between projected and (possibly accelerated) modulus-based matrix splitting methods for linear complementarity problems. In particular, first we show that some well-known projected splitting methods are equivalent, iteration by iteration, to some (accelerated) modulus-based matrix splitting methods with a specific choice of the parameter Ω. We then generalize this result to any Ω by formulating new classes of projected splitting methods and also provide a formal projection-based formulation for general (accelerated) modulus-based matrix splitting methods. Finally, we introduce and solve several test problems to evaluate also numerically the equivalence between the analyzed methods.