Solving system of inequalities via a smoothing homotopy method

In this paper, the system of nonlinear inequalities is considered. The problem is approximated by the parameterized smooth equations which is formed by Chen-Harker-Kanzow-Smale smoothing function. A smoothing homotopy method is proposed to solve the system of smooth equations. For almost all initial points in Euclidean space, the existence and convergence of the homotopy path is proved under certain weaker condition without assumption of the monotonicity. The numerical results illustrate that the method is effective.