NEURAL NETWORKS FOR SOLVING LINEAR INEQUALITY SYSTEMS

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.