Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities

Abstract

In this paper, we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.