A Global Convergence Method for Absolute Value Equations

We investigate an efficient method for solving the absolute value equation(AVE): Ax-|x|=b,which is a NP-hard problem,where A is an arbitrary n×n real matrix.In this paper,a smoothing Newton method which combines a smoothing function is proposed.When the interval matrix [A-I,A+I] is regular,we show that the proposed method is global convergence.