The problem of construction a piecewise linear discriminant function

The problem of numerical finding a piecewise linear function that separate the finite sets A and B is considered. For the purposes of strict separation of sets implies that the sets A and B have no common points, but their presence is not an obstacle for the proposed algorithm. Convexity of the discriminant functionorvoidintersectionofconvexhulls ofthesesets is not supposed. Naturallimitationis therequirement that the affine hull of the training set A È B include a recognizable element. For these purposes, we extend the main result of Benchekroun B., Falk James E. [1], which was a formalization of partitions Delaunay by means of linear programming. In this note we show that the condition of non-empty interior of convex hull the A È B can be removed while maintaining extreme properties of Delaunay partitions.