A Novel Transforming Function for Nonlinear Equations

In this paper, we propose a new global optimization approach based on filled function method to solve box-constrained systems of nonlinear equations. The filled function method consists of two phases: local minimization and filling. The method iterates from one local minimum to a better one. In each iteration, we construct a filled function that attains strict local maximum at the current solution. A local minimizer of the filled function leads to a new solution of reduced objective function value. Iteration follows in this manner to obtain the roots of (SNE). A solution algorithm based on this filled function is given. A numerical test is made. The computational results demonstrate that the proposed approach is efficient and reliable.