  Optimizations of atomic positions belong to the most commonly performed tasks
in electronic structure calculations. Many simulations like global minimum
searches or characterizations of chemical reactions require performing hundreds
or thousands of minimizations or saddle computations. To automatize these
tasks, optimization algorithms must not only be efficient, but also very
reliable. Unfortunately computational noise in forces and energies is inherent
to electronic structure codes. This computational noise poses a sever problem
to the stability of efficient optimization methods like the limited-memory
Broyden-Fletcher-Goldfarb-Shanno algorithm. We here present a technique that
allows obtaining significant curvature information of noisy potential energy
surfaces. We use this technique to construct both, a stabilized quasi-Newton
minimization method and a stabilized quasi-Newton saddle finding approach. We
demonstrate with the help of benchmarks that both the minimizer and the saddle
finding approach are superior to comparable existing methods.
