Black-Box Approximation and Optimization with Hierarchical Tucker
  Decomposition
Gleb Ryzhakov Andrei Chertkov Artem Basharin Ivan Oseledets
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.