1. A method for optimizing expensive functions with expensive nonlinear constraints, comprising: a1) partitioning constraints to an expensive function into inexpensive and expensive constraints; a2) selecting sample data for evaluating the expensive function of a simulation; b) generating, by a computer processor, a function proxy model for the expensive function using an approximation scheme, wherein the expensive function is an objective function and the function proxy model models the objective function; c1) generating, by the computer processor, a constraint proxy model for an expensive nonlinear constraint associated with the expensive function, wherein generating the constraint proxy model comprises replacing at least one expensive equality constraint with at least one less expensive constraint proxy, and wherein each constraint proxy is distinct from the function proxy model; c2) incorporating the at least one expensive constraint proxy into the constraints to the expensive function; d) calculating a first solution point for the simulation using at least both the function proxy model for the objective function and the constraint proxy model as a constraint; e) evaluating, by the computer processor, 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.