Abstract
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.
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