# On computing with some convex relaxations for the maximum-entropy sampling problem

arXiv: https://arxiv.org/abs/2112.14291 · HTML: https://mlsanity.com/paper/2112.14291/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2021.

## Built on by (most cited first, 2 of 2)

- [Parameter-Free Non-Ergodic Extragradient Algorithms for Solving Monotone Variational Inequalities](https://mlsanity.com/paper/2604.07662/) (2026)
- [The hyper-scaled NLP bound for maximum-entropy remote sampling](https://mlsanity.com/paper/2601.20970/) (2026)

## Abstract (arXiv)

Based on a factorization of an input covariance matrix, we define a mild generalization of an upper bound of Nikolov (2015) and Li and Xie (2020) for the NP-Hard constrained maximum-entropy sampling problem (CMESP). We demonstrate that this factorization bound is invariant under scaling and also independent of the particular factorization chosen. We give a variable-fixing methodology that could be used in a branch-and-bound scheme based on the factorization bound for exact solution of CMESP. We report on successful experiments with a commercial nonlinear-programming solver. We further demonstrate that the known "mixing" technique can be successfully used to combine the factorization bound with the factorization bound of the complementary CMESP, and also with the "linx bound" of Anstreicher (2020).