To solve Problem (PE), we have developed the CrystalEstimator program which leverages gradientbased optimisation algorithms to solve the outer problem. CrystalEstimator interfaces with CSO-RM to carry out the inner minimisations. Multistart capabilities are integrated into CrystalEstimator through a quasi-random initialisation sequence in order to increase the probability of finding the global optimal solution of this highly non-convex problem. However, there are a several problem-specific complications that require more-bespoke solutions.