The problem of finding the global minimum of a polynomial on a coordinate parallelepiped

The paper addresses the problem of finding the global minimum of a polynomial on a coordinate parallelepiped or on certain other sets with a simple structure.
To solve the problem, the Variable Elimination Algorithm for polynomial optimization problems described in the author's previous works is used.
It should be noted that the proposed method can be of practical significance only for problems of low dimensionality and for polynomials of not very high degree.
This is due to the fact that, when implementing the VEA, a large number of alternative problems may arise concerning the determination of real roots of polynomials, and these polynomials may have very high degrees.
Although, in theory, the Variable Elimination Algorithm is applicable to any polynomial optimization problems, there are often practically relevant problems that can be successfully solved using the proposed method.