On D-Optimality Based Trust Regions for Black-Box Optimization Problems

In this paper we show how techniques from response surface methodology and mathematical programming can be combined into a new sequential derivative-free approach for solving unconstrained deterministic black-box optimization problems.In this sequential derivative-free optimization approach local approximations of the underlying objective function are optimized within a trust region framework.If the points that determine the local approximations are located in such away that the approximations become bad, a geometry improving iteration is carried out instead of an objective improving iteration.We incorporate the D-optimality criterion, well-known in design of experiments, in our approach in two different ways.Firstly, it is used to define a trust region that adapts its shape to the locations of the points in which the objective function has been evaluated.Secondly, it determines an optimal geometry improving point.An attractive feature of our approach is that it is insensitive to affine transformations.