High-throughput experimentation (HTE) is an experimental paradigm that has shown potential for accelerating the evaluation of material systems by synthesizing a sample with a variation of material parameters and using parallel or fast serial characterization. Magnetron sputtering is one of the most widely used thin-film synthesis techniques in the HTE field. One major bottleneck for HTE magnetron sputtering is identifying appropriate sputtering conditions. Here, a Nelder Mead optimization procedure with soft constraints is used to determine sputtering conditions of a desired deposition rate distribution using a continuum based sputter model. The optimization procedure uses a multiple stage multistart method to overcome issues with initialization and multiple minima. The procedure was validated against a simulated thin film. The method was able to determine a gun power, gun tilt, and substrate height within 1% of the simulation sputtering conditions in 29.8 s. This result is 3-4 orders of magnitude faster than the traditional experimental approaches. The optimization was also validated against experimentally measured thickness profiles. During validation, the optimized sputtering conditions yielded a thickness profile that was within error of the experimental measurement and the model.