Generalized Kohn-Sham iteration on Banach spaces.

@article{Laestadius2018GeneralizedKI,
  title={Generalized Kohn-Sham iteration on Banach spaces.},
  author={Andre Laestadius and Markus Penz and Erik I Tellgren and Michael Ruggenthaler and Simen Kvaal and Trygve Helgaker},
  journal={The Journal of chemical physics},
  year={2018},
  volume={149 16},
  pages={
          164103
        }
}
A detailed account of the Kohn-Sham (KS) algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows us to rigorously introduce, in contrast to the common unregularized approach, a well-defined KS iteration scheme. Convergence in a weak sense is then proven. This… 
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