On D-optimality based trust regions for black-box optimization problems

Various sequential derivative-free optimization algorithms exist for solving black-box optimization problems. Two important building blocks in these algorithms are the trust region and the geometry improvement. In this paper, we propose to incorporate the D-optimality criterion, well known in the design of experiments, into these algorithms 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 is used to determine an optimal geometry-improving point. The proposed trust region and geometry improvement can both be implemented into existing sequential algorithms.