 
Summary: NEURAL NETWORK TRAINING VIA QUADRATIC OPTIMIZATION
Michael A. Satton' and PanosJ. Antsaklis2
'Cardemcl Division Code 1941
Naval SurfaceWarfaceCenter
Bethesda.Maryland 20084
Abstract  A new technique using quadratic optimization is proposed to find the
weights of a single neuron, or a singlelayer neural network, and extended to the
multilayer neural network. It is proposed here to fuui the weights for a neuron
by minimizing a cost function that is quadratic with respect to the neuron's
weights and to use these weights as an answer for minimizing a cost function
that is quadratic with respect to the neuron's outputs. Previous methods, such as
the least mean squares algorithm which is a grldient descent method and a
precursor of the backpropagation algorithm, iteratively find weights for the
neuron which minimiiz the eOst function directly involving the nonlinearity of
the neuron. By backpropagating the output error through the neural networks
layers, the proposed method is extended to the multilayer neural network. The
described Quadratic Optimization Algorithm for the multilayer neural network
mds to work best for classification problems and tends to achieve successful
results in a single iteration.
I INTRODUCTION
