Perspective on Moreau-Yosida Regularization in Density-Functional Theory

TL;DR

This paper discusses how Moreau-Yosida regularization enhances the mathematical foundation and reformulation of density-functional theory, linking it to classical field theories and improving inversion schemes.

Contribution

It provides a comprehensive perspective on the multiple roles of Moreau-Yosida regularization in density-functional theory and explores future development avenues.

Findings

Reformulates density-functional theory using Moreau-Yosida regularization.

Links regularization to classical field theories through topology choices.

Improves density-potential inversion schemes.

Abstract

Within density-functional theory, 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 density-functional theory alongside possibilities for their future development.