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A globally optimum minimum stored energy optimization strategy is implemented to design actively shielded superconducting magnet configurations used in high-field applications. The current density map is first obtained and used as a foundation for the magnet configurations by placing coils at current density local extremities. Optimized current density maps based on the stored energy formulation along with final magnet arrangements are provided to illustrate the findings. In this work, the focus was on compact superconducting magnets as measured by physical size and system footprint for given magnetic field properties inside the imaging region. The process of obtaining the current density maps proposed here over the given magnet domain, where superconducting coils are laid out, suggests that peak current densities occur around the perimeter of the domain, where in the most compact designs, with the domain length less than 1 m, the current direction alternates amongst adjacent coils. To reduce the peak magnetic field to acceptable levels on the superconductors in high-field designs, the size of the magnet domain is made larger, to the extent that the current densities no longer alternate between coils.