A method for optimizing expensive functions with expensive nonlinear constraints. The method includes selecting sample data for evaluating an expensive function of a simulation, generating a function proxy model for the expensive function and a constraint proxy model for an expensive nonlinear constraint of the expensive function using an approximation scheme, calculating a first solution point for the simulation using the proxy models, and evaluating the expensive function at the first solution point using the sample data. When the expensive function and the proxy models do not converge at the first solution point, the method further includes adding the first solution point to the sample data for updating the proxy models. The method further includes repeating the calculation and evaluation of solution points until the expensive function and the proxy models converge and, following convergence, identifying an optimal solution of the function proxy model and the constraint proxy model.