The Square-Newton iteration for linear complementarity problem

Abstract

For solving the linear complementary problem (LCP), a series of modulus-based matrix splitting iteration methods are proposed. Those methods are based on the splitting of coefficient matrix. We proposed a Square-Newton method which combine the Newton method with the non-negativity of square number to solve the LCP without the matrix splitting. This method can efficient solve LCP and has quadratic convergence. The effectiveness of the Square-Newton is confirmed by some numerical experiments.