Extension of Newton's Method to Mixed Systems of Nonlinear Equations and Inequalities.

The paper shows how Newtons method may be extended, by using linear programming, to solve mixed systems of nonlinear equations and inequalities of the form gx or 0, fx 0. The number of equations andor inequalities need not equal the number of variables, and the solutions need not be unique or isolated. An extension of the Kantorovich theorem is proved for this method it shows, among other things, that the same quadratic rate of convergence holds for this technique as for the conventional version of Newtons method. Author