Black-Box Approximation and Optimization with Hierarchical Tucker Decomposition

We develop a new method HTBB for the multidimensional black-box approximation and gradient-free optimization, which is based on the low-rank hierarchical Tucker decomposition with the use of the MaxVol indices selection procedure. Numerical experiments for 14 complex model problems demonstrate the robustness of the proposed method for dimensions up to 1000, while it shows significantly more accurate results than classical gradient-free optimization methods, as well as approximation and optimization methods based on the popular tensor train decomposition, which represents a simpler case of a tensor network.