Mathematical model of optimal triangulation

The problem of synthesis of optimal planar convex triangulation is formalized. This problem arises in different applications of informatics problems and is very actual for its sections such as computer graphics and geographical information systems. The mathematical model is represented as an extremum problem with infinite number of constraints, as a minimax problem with bound variables, and as an extremum problem with additional constraints on line segments intersections of triangulation with limited number of constraints. By putting idempotent limitations on Boolean variables, the initial integer-valued problem could be solved as a general mathematical programming problem on a continuum set of answers. In addition, the comparison of results obtained by the greedy algorithm based on the represented model and Delaunay triangulation is provided.