  In this paper (part 1), we describe a derivative-free trust-region method for
solving unconstrained optimization problems. We will discuss a method when we
relax the model order assumption and use artificial neural network techniques
to build a computationally relatively inexpensive model. We directly find an
estimate of the objective function minimizer without explicitly constructing a
model function. Therefore, we need to have the neural-network model
derivatives, which can be obtained simply through a back-propagation process.
