In this work, we develop a novel motion optimization system suitable for offline generation of complex, physically realistic character animation. Given a rough input motion, the system is capable of automatically adjusting it to match position and physics constraints while simultaneously optimizing it with respect to an objective function. The chief advantage our system has over similar prior work is that it requires no derivatives of the motion or objective function; the only inputs required are a forward simulator, objective and constraint functions, and an initial guess. The optimization is accomplished by a novel trust-region based optimization framework using reduced quadratic interpolation models. Removing the derivative requirements gives the system substantially more flexibility and ease of use than previous systems, while still providing comparable efficiency and results.