Many physical phenomena in engineering design can be described by computational models of high physical fidelity or numerical accuracy.

Optimization with high-fidelity simulations gives rise to large-scale nonlinear programming problems (NLP) due to the large number of state variables and the associated computational cost of solving (coupled) differential equations that govern the behavior of the system. Straightforward use of high-fidelity models, such as the Navier-Stokes equations or those based on fine computational meshes, in iterative procedures can be prohibitively expensive. We discuss a first-order, variable-fidelity model management scheme for solving optimization problems whose function evaluations involve outputs of simulations. The approach reduces the cost of optimization by systematically using lower-fidelity models or surrogates, with occasional recourse to high-fidelity computations for model re-calibration. Convergence to high-fidelity results is maintained. We discuss computation with variable-resolution and variable physical fidelity models, as well as a variety of response surface approximations.