Many systems and processes, both natural and artificial, may be described by parameter-driven mathematical and physical models. We introduce a generally applicable Stochastic Optimization Framework (SOF) that can be interfaced to or wrapped around such models to optimize model outcomes by effectively "inverting" them. The Visual and Autonomous Exploration Systems Research Laboratory (http://autonomy.caltech.edu) at the California Institute of Technology (Caltech) has long-term experience in the optimization of multi-dimensional systems and processes. Several examples of successful application of a SOF are reviewed and presented, including biochemistry, robotics, device performance, mission design, parameter retrieval, and fractal landscape optimization. Applications of a SOF are manifold, such as in science, engineering, industry, defense & security, and reconnaissance/exploration.