# Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions

## TL;DR

This paper proves that a regularized Kohn-Sham iteration with adaptive damping reliably converges to the true ground-state density in finite-dimensional density-functional theory.

## Contribution

It demonstrates convergence of a regularized Kohn-Sham iteration with adaptive damping in finite dimensions, ensuring correct ground-state density calculation.

## Key findings

- Convergence is guaranteed with Moreau-Yosida regularization.
- Adaptive damping ensures stability and convergence.
- The method accurately finds the ground-state density.

## Abstract

The exact Kohn-Sham iteration of generalized density-functional theory in finite dimensions witha Moreau-Yosida regularized universal Lieb functional and an adaptive damping step is shown toconverge to the correct ground-state density.