Representation of a Polynomial Function as a Difference of Convex Polynomials, with an Application

One of the main problems in global optimization is the multiextremal global optimization in which an objective function has several local minima and at least one global minimum. To deal with this problem, it is useful to have a convex difference representation of all the functions involved, as this allows for employing so-called d.c. optimization techniques.Procedures that permit the calculation of the polynomial convex difference representation of any polynomial are presented and analyzed here, and an application is made to a real problem whose functions are polynomials of degrees up to four.