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Robust Linear Programming Discrimination Of Two Linearly Inseparable Sets
, 1992
"... INTRODUCTION We consider the two pointsets A and B in the ndimensional real space R n represented by the m \Theta n matrix A and the k \Theta n matrix B respectively. Our principal objective here is to formulate a single linear program with the following properties: (i) If the convex hulls of A ..."
Abstract

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INTRODUCTION We consider the two pointsets A and B in the ndimensional real space R n represented by the m \Theta n matrix A and the k \Theta n matrix B respectively. Our principal objective here is to formulate a single linear program with the following properties: (i) If the convex hulls of A and B are disjoint, a strictly separating plane is obtained. (ii) If the convex hulls of A and B intersect, a plane is obtained that minimizes some measure of misclassification points, for all possible cases. (iii) No extraneous constraints are imposed on the linear program that rule out any specific case from consideration. Most linear programming formulations 6,5,12,4 have property (i)