In the ongoing PhD project of Benjamin Peters a novel approach to Polynomial Optimization was developed. It uses monomial patterns and is a generalization of approaches that have been used in the disjoint communities of numerical global optimization (e.g., BARON) and the sums-of-squares optimizers. The novel general point of view facilitates the design and usage of sparse approximation patterns and decompositions of large semi-definite-programs into several small conic optimization problems. The goal of the proposed PhD project is two-fold. First, the algorithm and its prototypical implementation shall be improved with a competitive general polynomial optimization solver in mind. Second, the transfer of the monomial pattern approach to the global optimization of optimal control problems (in the spirit of Henrion and Lasserre) shall be investigated. In this context also warmstarting across approximation levels might play a role.