# Convex relaxation approaches for strictly correlated density functional theory

arXiv: https://arxiv.org/abs/1808.04496 · HTML: https://mlsanity.com/paper/1808.04496/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2018.

## Built on by (most cited first, 1 of 1)

- [Genetic column generation: Fast computation of high-dimensional multi-marginal optimal transport problems](https://mlsanity.com/paper/2103.12624/) (2021)

## Abstract (arXiv)

In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of N-representable 2-marginals and 3-marginals, which in turn provide lower bounds to the energy. We further propose rounding schemes to obtain upper bound to the energy. Numerical experiments demonstrate a gap of the order of 10-3 to 10-2 between the upper and lower bounds. The Kantorovich potential of the multi-marginal transport problem is also approximated with a similar accuracy.