A class of inexact modified Newton-type iteration methods for solving the generalized absolute value equations

In Wang et al. (J. Optim. Theory Appl., \textbf{181}: 216--230, 2019), a class of effective modified Newton-tpye (MN) iteration methods are proposed for solving the generalized absolute value equations (GAVE) and it has been found that the MN iteration method involves the classical Picard iteration method as a special case. In the present paper, it will be claimed that a Douglas-Rachford splitting method for AVE is also a special case of the MN method. In addition, a class of inexact MN (IMN) iteration methods are developed to solve GAVE. Linear convergence of the IMN method is established and some specific sufficient conditions are presented for symmetric positive definite coefficient matrix. Numerical results are given to demonstrate the efficiency of the IMN iteration method.