A derivative-free method for the system of nonlinear equations

There are many techniques to attack the system of nonlinear equations (SNE). When it is very difficult to calculate derivative or there exist no derivatives for some SNE, some approaches without derivatives are suitable. In this work, we extend generalized pattern search (GPS) approach of Torczon's to handle system of nonlinear equations. To find a trial point from current point, we test some points in a mesh consisting of several directions. In every step, some norm of the system of nonlinear equation is required to reduce.