Cutting methods in $E^{n+1}$ for global optimization of a class of functions

A class of functions that attain their minima on a compact subset of the $n$-dimensional Euclidean space $E^n$ is introduced. This is a rather broad functional class, which is stable with respect to operations commonly occurring in optimization. The functions in this class are a convenient tool in the formal description of numerous applied problems. Moreover, reasonably efficient methods can be developed for finding global minima of such functions on a compact set. One such method is discussed in this paper.