RF deep hyperthermia systems make use of phased arrays of applicators in order to heat tumors selectively while maintaining healthy tissue at normal temperatures. A new method for the array synthesis is proposed based on the identification of targets to be heated (tumors) and targets to be prevented from excess electromagnetic radiation. The best array feed for each target is found from the solution of the eigenvector problem for a positive definite Hermitian matrix defined for that target. The optimal feed in a global sense then results from a trade-off of the best feeds of individual targets enforced through minimization of an objective function aimed at weighting the distances of the globally optimal feed from the feed vectors optimized for each target separately. An application to the heating of a pelvis is provided as an example.