Model Construction for Convex-Constrained Derivative-Free Optimization

In model-based derivative-free optimisation algorithms, black-box functions are typically approximated using polynomial interpolation models. Most existing model-based DFO methods for constrained optimisation assume the ability to construct sufficiently accurate interpolation models, but this is not always achievable when sampling only feasible points. In this talk, I will outline a new approximation theory for linear and quadratic interpolation models in the presence of convex constraints.