Perspective on Moreau–Yosida regularization in density-functional theory

Within density-functional theory (DFT), Moreau–Yosida regularization enables both a reformulation of the theory and a mathematically well-defined definition of the Kohn–Sham approach. It is further employed in density–potential inversion schemes and, through the choice of topology for the density and potential space, can be directly linked to classical field theories. This perspective collects various appearances of the regularization technique within DFT alongside possibilities for their future development.