Abstract: An algorithm applied in the radiological treatment of tumors which minimizes a cost function which is quadratic in the residual between the prescribed dose distribution and the calculated resultant dose. Possible treatment arcs must be stipulated and the algorithm includes an automatic technique for multiple iso-center selection. One overall strategy can be specification of an unrealistically large number of beams (or arcs) and systematic deletion of those beams having the smallest recommended weights until a practical solution is obtained. Tumor, non-tumor, and avoidance areas can be defined. Constrained matrix immersion results in optimum weights and dosage in the treatment of the tumor.