  A fast and reliable geometry optimization algorithm is presented that
optimizes atomic positions and lattice vectors simultaneously. Using a series
of benchmarks, it is shown that the method presented in this paper outperforms
in most cases the standard optimization methods implemented in popular codes
such as QUANTUM ESPRESSO and VASP. To motivate the variable cell shape
optimization method presented in here, the eigenvalues of the lattice Hessian
matrix are investigated thoroughly. It is shown that they change depending on
the shape of the cell and the number of particles inside the cell. For certain
cell shapes the resulting condition number of the lattice matrix can grow
quadratically with respect to the number of particles. By a coordinate
transformation which can be applied to all variable cell shape optimization
methods, the undesirable conditioning of the lattice Hessian matrix is
eliminated.
