A rigorous framework for optimization of expensive functions by surrogates

The goal of the research reported here is to develop rigorous optimization algorithms to apply to some engineering design problems for which direct ap plication of traditional optimization approaches is not practical. This pap er presents and analyzes a framework for generating a sequence of approxima tions to the objective function and managing the use of these approximation s as surrogates for optimization. The result is to obtain convergence to a minimizer of an expensive objective function subject to simple constraints. The approach is widely applicable because it does not require, or even exp licitly approximate, derivatives of the objective. Numerical results are pr esented for a 31-variable helicopter rotor blade design example and for a s tandard optimization test example.