  Convexification is a core technique in global polynomial optimization.
Currently, there are two main approaches competing in theory and practice: the
approach of nonlinear programming and the approach based on positivity
certificates from real algebra. The former are comparatively cheap from a
computational point of view, but typically do not provide tight relaxations
with respect to bounds for the original problem. The latter are typically
computationally expensive, but do provide tight relaxations. We embed both
kinds of approaches into a unified framework of monomial relaxations. We
develop a convexification strategy that allows to trade off the quality of the
bounds against computational expenses. Computational experiments show very
encouraging results.
