On the Convergence of a New Smoothing Levenberg-Marquardt Method for the Nonlinear Inequalities

The least l₂-norm solution for a possibly inconsistent system of nonlinear inequalities is studied in this paper. By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions. Then a smoothing Levenberg-Marquardt method are applied to solve the parameterized optimization problems. The global convergence of the proposed method are established under some weak conditions. Numerical results show that the methods perform well.