  In the construction of a stellarator, the manufacturing and assembling of the
coil system is a dominant cost. These coils need to satisfy strict engineering
tolerances, and if those are not met the project could be canceled as in the
case of the National Compact Stellarator Experiment (NCSX) project [25].
Therefore, our goal is to find coil configurations that increase construction
tolerances without compromising the performance of the magnetic field. In this
paper, we develop a gradient-based stochastic optimization model which seeks
robust stellarator coil configurations in high dimensions. In particular, we
design a two-step method: first, we perform an approximate global search by a
sample efficient trust-region Bayesian optimization; second, we refine the
minima found in step one with a stochastic local optimizer. To this end, we
introduce two stochastic local optimizers: BFGS applied to the Sample Average
Approximation and Adam, equipped with a control variate for variance reduction.
Numerical experiments performed on a W7-X-like coil configuration demonstrate
that our global optimization approach finds a variety of promising local
solutions at less than 0.1% of the cost of previous work, which considered
solely local stochastic optimization.
