The entropic barrier is $n$-self-concordant
arXiv:2112.10947v116 citations
Originality Synthesis-oriented
AI Analysis
This provides a tight theoretical bound in convex optimization, but it is an incremental improvement for specialists in barrier methods.
The authors proved that the entropic barrier on a convex body in ℝⁿ is exactly n-self-concordant, improving a previous bound of (1+o(1))n, by leveraging the dimensional Brascamp-Lieb inequality.
For any convex body $K \subseteq \mathbb R^n$, S. Bubeck and R. Eldan introduced the entropic barrier on $K$ and showed that it is a $(1+o(1)) \, n$-self-concordant barrier. In this note, we observe that the optimal bound of $n$ on the self-concordance parameter holds as a consequence of the dimensional Brascamp-Lieb inequality.