Neural nets for massively parallel optimization

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Abstract
To apply massively parallel processing systems to the solution of large scale optimization problems it is desirable to be able to evaluate any function f(z), z (epsilon) Rn in a parallel manner. The theorem of Cybenko, Hecht Nielsen, Hornik, Stinchcombe and White, and Funahasi shows that this can be achieved by a neural network with one hidden layer. In this paper we address the problem of the number of nodes required in the layer to achieve a given accuracy in the function and gradient values at all points within a given n dimensional interval. The type of activation function needed to obtain nonsingular Hessian matrices is described and a strategy for obtaining accurate minimal networks presented.

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