In medical magnetic resonance imaging, parallel radio frequency excitation pulses have to respect a large number of specific absorption rate constraints. Geometrically, each of these constraints can be interpreted as a complex, centered ellipsoid. We propose to replace a collection of such constraints by the single constraint which corresponds to the associated maximum volume inscribed ellipsoid and implies all original constraints. We describe how to compute this ellipsoid via convex programming. Examples show that this reduction has very short computation times but cuts away parts of the feasible power domain.