On some computational problems of constructing piecewise linear approximations of functions with the Delaunay property

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In the article, we discuss issues related to the construction of a piecewise linear approximation of some function, information about which is limited to its values at given points from some finite set. A wide range of tasks from various fields of knowledge leads to such a formulation. A feature of the approach to the problem under consideration is the application of the Delaunay partition methodology, based on linear programming technologies. The goal is to extend this promising methodology to a more wide class of problems without requiring that the convex hull of the set is bodily.