  In this paper, we present a flow-based method for global optimization of
continuous Sobolev functions, called Stein Boltzmann Sampling (SBS). SBS
initializes uniformly a number of particles representing candidate solutions,
then uses the Stein Variational Gradient Descent (SVGD) algorithm to
sequentially and deterministically move those particles in order to approximate
a target distribution whose mass is concentrated around promising areas of the
domain of the optimized function. The target is chosen to be a properly
parametrized Boltzmann distribution. For the purpose of global optimization, we
adapt the generic SVGD theoretical framework allowing to address more general
target distributions over a compact subset of $\mathbb{R}^d$, and we prove
SBS's asymptotic convergence. In addition to the main SBS algorithm, we present
two variants: the SBS-PF that includes a particle filtering strategy, and the
SBS-HYBRID one that uses SBS or SBS-PF as a continuation after other particle-
or distribution-based optimization methods. A detailed comparison with
state-of-the-art methods on benchmark functions demonstrates that SBS and its
variants are highly competitive, while the combination of the two variants
provides the best trade-off between accuracy and computational cost.
