A filter algorithm for nonlinear systems of equalities and inequalities

In this paper, we propose a filter algorithm for nonlinear systems of equalities and inequalities. In the algorithm, the systems of nonlinear equalities and inequalities are transformed into a nonlinear programming problem. The new algorithm uses the non-monotone technique in conjunction with filter idea and a global line search strategy that ensures convergence from any starting point. Under mild conditions, global convergence and local superlinear convergence rate are obtained. Numerical results demonstrate that the new algorithm is effective.