  We are interested in the design of generative networks. The training of these
mathematical structures is mostly performed with the help of adversarial
(min-max) optimization problems. We propose a simple methodology for
constructing such problems assuring, at the same time, consistency of the
corresponding solution. We give characteristic examples developed by our
method, some of which can be recognized from other applications, and some are
introduced here for the first time. We present a new metric, the likelihood
ratio, that can be employed online to examine the convergence and stability
during the training of different Generative Adversarial Networks (GANs).
Finally, we compare various possibilities by applying them to well-known
datasets using neural networks of different configurations and sizes.
