A new method of calculating beam emittances at the extraction point of a particle accelerator is presented. The technique uses the optimization programs NPSOL and MINOS developed at Stanford University in order to determine the initial values of beam size, divergence and correlation parameters (i.e. beam sigma matrix, r ij ) that best fit measured beam parameters. These r ij elements are then used to compute the Twiss parameters a, b, and the phase space area, e, of the beam at the extraction point. Beam size measurements in X and Y throughout the transport line were input to the optimizer along with the magnetic elements of bends, quads, and drifts. The r ij parameters were optimized at the acceleratorΓs extraction point by finding the best agreement between these measured beam sizes and those predicted by TRANSPORT. This expands upon a previous study in which a ''trial and error'' technique was used instead of the optimizer software, and which yielded similar results. The Particle Beam Optics Laboratory (PBO Lab TM ) program used for this paper integrates particle beam optics and other codes into a single intuitive graphically-based computing environment. This new software provides a seamless interface between the NPSOL and MINOS optimizer and TRANS-PORT calculations. The results of these emittance searches are presented here for the eight clinical energies between 70 and 250 MeV currently being used at LLUMC.