A nonmonotone smoothing Newton method for system of nonlinear inequalities based on a new smoothing function

Abstract

In this paper, a nonmonotone smoothing Newton method is proposed for solving system of nonlinear inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations $$H_u(z)=0$$ . A smoothing Newton method is developed for solving the system of nonlinear inequalities by adopting a new nonmonotone line search scheme. Under mild assumptions, our algorithm is shown to possess global and local quadratic convergence properties. Some preliminary numerical results are reported.