1. A method for optimizing expensive functions with expensive nonlinear constraints, comprising: a) selecting sample data for evaluating an expensive function of a simulation; b) generating a function proxy model for the expensive function using an approximation scheme; c) generating a constraint proxy model for an expensive nonlinear constraint associated with the expensive function using the approximation scheme; d) calculating a first solution point for the simulation using the function proxy model and the constraint proxy model; e) evaluating the expensive function of the simulation at the first solution point from the function proxy model and constraint proxy model using the sample data; f) when the expensive function, the function proxy model, and the constraint proxy model do not converge at the first solution point: adding the first solution point to the sample data to obtain updated sample data; and updating the function proxy model and the constraint proxy model based on the updated sample data; g) repeating steps d) through f) until the expensive function, the function proxy model, and the constraint proxy model converge at the first solution point; and h) when the expensive function, the function proxy model, and the constraint proxy model converge at the first solution point, identifying an optimal solution of the function proxy model and the constraint proxy model.