Finitely convergent ε-generalized projection algorithm for nonlinear systems

This paper discusses the solving methods for nonlinear systems. Firstly, basing on the technique of ε-generalized projection and a new line search technique, we present a new algorithm for solving systems of nonlinear inequalities. At each iteration of the proposed algorithm, the search direction is obtained by only one new explicit ε-generalized projection formula. Then under some necessary assumptions, the algorithm is proved to not only possess global convergence but also can produce a solution in a finite number of iterations. Finally, the algorithm is extended to the systems of nonlinear inequalities and equalities, and some preliminary numerical results are reported.