A regularized smoothing-type algorithm for solving a system of inequalities with a -function

The system of nonlinear inequalities is studied in this paper. By using the Chen–Harker–Kanzow–Smale smoothing function, the problem is approximated by a family of parameterized smooth equations. A regularized smoothing Newton algorithm is proposed to solve the smooth equations. We prove that the proposed algorithm converges globally and superlinearly under mild conditions. Furthermore, the algorithm has local quadratic convergence under suitable conditions. Preliminary numerical experiments are reported to show the efficiency of the algorithm.