  In this paper, we modify and apply the recently introduced Mixed Newton
Method, which is originally designed for minimizing real-valued functions of
complex variables, to the minimization of real-valued functions of real
variables by extending the functions to complex space. We show that arbitrary
regularizations preserve the favorable local convergence properties of the
method, and construct a special type of regularization used to prevent
convergence to complex minima. We compare several variants of the method
applied to training neural networks with real and complex parameters.
