  The convergence of many numerical optimization techniques is highly dependent
on the initial guess given to the solver. To address this issue, we propose a
novel approach that utilizes tensor methods to initialize existing optimization
solvers near global optima. Our method does not require access to a database of
good solutions. We first transform the cost function, which depends on both
task parameters and optimization variables, into a probability density
function. Unlike existing approaches, the joint probability distribution of the
task parameters and optimization variables is approximated using the Tensor
Train model, which enables efficient conditioning and sampling. We treat the
task parameters as random variables, and for a given task, we generate samples
for decision variables from the conditional distribution to initialize the
optimization solver. Our method can produce multiple solutions (when they
exist) faster than existing methods. We first evaluate the approach on
benchmark functions for numerical optimization that are hard to solve using
gradient-based optimization solvers with a naive initialization. The results
show that the proposed method can generate samples close to global optima and
from multiple modes. We then demonstrate the generality and relevance of our
framework to robotics by applying it to inverse kinematics with obstacles and
motion planning problems with a 7-DoF manipulator.
