  Numerical optimization is an important tool in the field of computational
physics in general and in nano-optics in specific. It has attracted attention
with the increase in complexity of structures that can be realized with
nowadays nano-fabrication technologies for which a rational design is no longer
feasible. Also, numerical resources are available to enable the computational
photonic material design and to identify structures that meet predefined
optical properties for specific applications. However, the optimization
objective function is in general non-convex and its computation remains
resource demanding such that the right choice for the optimization method is
crucial to obtain excellent results. Here, we benchmark five global
optimization methods for three typical nano-optical optimization problems:
\removed{downhill simplex optimization, the limited-memory
Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm
optimization, differential evolution, and Bayesian optimization}
\added{particle swarm optimization, differential evolution, and Bayesian
optimization as well as multi-start versions of downhill simplex optimization
and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm}. In
the shown examples from the field of shape optimization and parameter
reconstruction, Bayesian optimization, mainly known from machine learning
applications, obtains significantly better results in a fraction of the run
times of the other optimization methods.
