  We implemented a geometry optimizer based on Gaussian process regression
(GPR) to find minimum structures on potential energy surfaces. We tested both a
two times differentiable form of the Mat\'{e}rn kernel and the squared
exponential kernel. The Mat\'{e}rn kernel performs much better. We give a
detailed description of the optimization procedures. These include overshooting
the step resulting from GPR in order to obtain a higher degree of interpolation
vs. extrapolation. In a benchmark against the L-BFGS optimizer of the DL-FIND
library on 26 test systems, we found the new optimizer to generally reduce the
number of required optimization steps.
