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

Abstract

The vertical linear complementarity problem (VLCP) with an arbitrary number l 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.