Response surface computation via simulation in the presence of convexity

We consider the problem of computing a response surface when the underlying function is known to be convex. We introduce a methodology that incorporates the convexity into the function estimator. The proposed response surface estimator is formulated as a finite dimensional quadratic program and exhibits convergence properties as a global approximation to the true function. Numerical results are presented to illustrate the convergence behavior of the proposed estimator and its potential application to simulation optimization.