  This paper presents a new approach to quadrify a polynomial programming
problem, i.e. reduce the polynomial program to a quadratic program, before
solving it. The proposed approach, QUAD-RLT, exploits the
Reformulation-Linearization Technique (RLT) structure to obtain smaller
relaxations that can be solved faster and still provide high quality bounds.
QUAD-RLT is compared to other quadrification techniques that have been
previously discussed in the literature. The paper presents theoretical as well
as computational results showing the advantage of QUAD-RLT compared to other
quadrification techniques. Furthermore, rather than quadrifying a polynomial
program, QUAD-RLT is generalized to reduce the degree of the polynomial to any
degree. Computational results show that reducing the degree of the polynomial
to a degree that is higher than two provides computational advantages in
certain cases compared to fully quadrifying the problem. Finally, QUAD-RLT
along with other quadrification/degree reduction schemes are implemented and
made available in the freely available software RAPOSa.
