In this paper we analyze different schemes for obtaining gradient estimates when the underlying function is noisy. Good gradient estimation is e.g. important for nonlinear programming solvers. As an error criterion we take the norm of the difference between the real and estimated gradients. This...

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field...

This article presents a novel combination of robust optimization developed in mathematical programming, and robust parameter design developed in statistical quality control. Robust parameter design uses metamodels estimated from experiments with both controllable and environmental inputs...