Generalized modulus-based matrix splitting algorithm with Anderson acceleration strategy for vertical linear complementarity problems

The vertical linear complementarity problem (VLCP) with an arbitrary number.. of matrices is related to many practical problems, of which the state-of-the-art modulus-based matrix splitting (MMS) method is proved to be an efficient solver. Enlightened by the Anderson acceleration which is a well-established and simple technique for speeding up fixed point iteration solvers with countless applications, we propose an Anderson accelerated generalized modulus-based matrix splitting (AA+GMMS) method for solving the VLCP. We particularly analyze the AA+GMMS method for the problem with l = 2 and then generalize the method to any l. More importantly, the convergence theorems and theoretical optimal parameters of the MMS, AA+GMMS methods with any l are obtained in the positive definite case. Eventually, numerical experiments are given to demonstrate the effectiveness of the AA+GMMS method which significantly accelerates the original MMS method. In particular, we explore the parameters involved in the AA+GMMS method, and they have a small extent of impact on the suggested method, reinforcing that the AA+GMMS method is highly efficient.