In this paper a neural network approach to the on-line solution of lin
ear inequality systems is considered. Three different techniques are d
iscussed and for each technique a novel neural network implementation
is proposed. The first technique is a standard penalty method implemen
ted as an analog neural network. The second technique is based on the
transformation of inequality constraints into equality constraints wit
h simple bounds on the variables, The transformed problem is then solv
ed using least squares (LS) and least absolute values (LAV) optimisati
on criteria. The third technique makes use of the regularised total le
ast squares criterion (RTLS). For each technique a suitable neural net
work architecture and associated algorithm in the form of nonlinear di
fferential equations has been developed. The validity and performance
of the proposed algorithms has been verified by computer simulation ex
periments. The analog neural networks are deemed to be particularly we
ll suited for high throughput, real time applications.