First-order approximation and model management in optimization

We discuss first-order approximation and model management optimization, an approach to the optimization of systems governed by differential equations. Our approach tries to alleviate the expense of relying exclusively on high-fidelity simulations, e.g., the solution of the governing differential equations on very fine meshes or the use of very detailed physics, while still guaranteeing global convergence of the overall optimization process to a solution of the high-fidelity problem. We focus here on several model management methods and experience with their performance.