Pattern Classifier Design by Linear Programming
IEEE Transactions on Computers
The Accelerated Relaxation Method for Linear Inequalities
IEEE Transactions on Computers
An Algorithm for the Solution of Linear Inequalities
IEEE Transactions on Computers
IEEE Transactions on Computers
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A method for solving systems of linear inequalities, consistent and inconsistent, corresponding to the separable and nonseparable cases in pattern recognition is presented. Attempts are made to evaluate the speed and efficiency of the algorithm. It seems to compare in speed with the best algorithms for consistent systems of inequalities in the consistent case and retains remarkable speed in the inconsistent case. There are indications that in many cases it may be relied on to find a complete solution if several runs are taken, most runs achieving a nearly complete solution. The experimental evidence suggests that this is the most efficient and powerful method currently available for finding a solution which satisfies as many cases as possible in a set of linear inequalities.