  We consider a direct optimization approach for ensemble density functional
theory electronic structure calculations. The update operator for the
electronic orbitals takes the structure of the Stiefel manifold into account
and we present an optimization scheme for the occupation numbers that ensures
that the constraints remain satisfied. We also compare sequential and
simultaneous quasi-Newton and nonlinear conjugate gradient optimization
procedures, and demonstrate that simultaneous optimization of the electronic
orbitals and occupation numbers improve performance compared to the sequential
approach.
