Potential reduction interior point algorithm for absolute value equations

Potential reduction interior point algorithm is proposed for solving the NP-hard absolute value equations (AVE) Au - |u| = b. Under the condition that all the singular values of A are not less than one, the existence and uniqueness theorem of the solution to the AVE is presented by formulating absolute value equation as monotone linear complementary problem. Then we proposed potential reduction interior point algorithm to AVE based on the Newton direction and centering direction. We establish finite convergence of the method. Preliminary numerical results indicate that the potential reduction interior point method is promising.