Description of functionals that are minimized by \(\Phi\)-triangulations (Q2278243)

Conditions for functionals of sum type defined on the set of all triangulations of a finite subset of the points of the plane under which a triangulation satisfying the empty convex condition set (also called \(\Phi\)-triangulation) minimizes this functional are found. The same type of results are obtained in case of functionals of maximum type. As a consequence, the property of the Delone type triangulation class of providing a minimal value to the functionals of these types stands under the identified conditions.