Newton-type methods for solving vertical linear complementarity problems

In this paper, Newton-type methods are proposed to solve the vertical linear complementarity problems. This kind of methods is different from the existing iteration methods such as the modulus-based matrix splitting methods. By analyzing the sign pattern for the solution and reformulating the vertical linear complementarity problem to an equivalent system of nonlinear equations, we propose the Newton's method and a practical-Newton's method that combine the Newton's method and modulus-based matrix splitting method. Numerical experiments are given to show that these Newton-type methods have much higher efficiency than the existing modulus-based matrix splitting methods.