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Networks of neurons can perform computations that even modern computers find very difficult to simulate. Most of the existing artificial neurons and artificial neural networks are considered biologically unrealistic, nevertheless the practical success of the backpropagation algorithm and the powerful capabilities of feedforward neural networks have made neural computing very popular in several application areas. A challenging issue in this context is learning internal representations by adjusting the weights of the network connections. To this end, several first-order and second-order algorithms have been proposed in the literature. This paper provides an overview of approaches to backpropagation training, emphazing on first-order adaptive learning algorithms that build on the theory of nonlinear optimization, and proposes a framework for their analysis in the context of deterministic optimization. [ABSTRACT FROM AUTHOR]