  Conic optimization has recently emerged as a powerful tool for designing
tractable and guaranteed algorithms for non-convex polynomial optimization
problems. On the one hand, tractability is crucial for efficiently solving
large-scale problems and, on the other hand, strong bounds are needed to ensure
high quality solutions. In this research, we investigate the strengthening of
RLT relaxations of polynomial optimization problems through the addition of
nine different types of constraints that are based on linear, second-order
cone, and semidefinite programming to solve to optimality the instances of well
established test sets of polynomial optimization problems. We describe how to
design these conic constraints and their performance with respect to each other
and with respect to the standard RLT relaxations. Our first finding is that the
different variants of nonlinear constraints (second-order cone and
semidefinite) are the best performing ones in around $50\%$ of the instances.
Additionally, we present a machine learning approach to decide on the most
suitable constraints to add for a given instance. The computational results
show that the machine learning approach significantly outperforms each and
every one of the nine individual approaches.
