Universal Barrier is n-Self-Concordant
Not on the map. Why?
Abstract (arXiv)
This paper shows that the self-concordance parameter of the universal barrier on any n-dimensional proper convex domain is upper bounded by n. This bound is tight and improves the previous O(n) bound by Nesterov and Nemirovski. The key to our main result is a pair of new, sharp moment inequalities for s-concave distributions, which could be of independent interest.
Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Sep 2018.
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Citing papers per year: 2021: 1; 2022: 2; 2023: 1; 2024: 0; 2025: 1; 2026: 1.
6 papers.
- 2022Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Spacecited by 28
- 2023Best-of-Three-Worlds Linear Bandit Algorithm with Variance-Adaptive Regret Boundscited by 14
- 2021The entropic barrier is n-self-concordantcited by 6
- 2026Beyond the d2.5-mixing bound for Dikin walks on polytopescited by 2
- 2025Self-Concordant Perturbations for Linear Banditscited by 1
- 2022Decomposable Non-Smooth Convex Optimization with Nearly-Linear Gradient Oracle Complexitycited by 0
- 2026Beyond the d2.5-mixing bound for Dikin walks on polytopes15 Jul 2026
- 2025Self-Concordant Perturbations for Linear Bandits28 Oct 2025
- 2023Best-of-Three-Worlds Linear Bandit Algorithm with Variance-Adaptive Regret Bounds24 Feb 2023
- 2022Decomposable Non-Smooth Convex Optimization with Nearly-Linear Gradient Oracle Complexity7 Aug 2022
- 2022Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space3 Feb 2022
- 2021The entropic barrier is n-self-concordant21 Dec 2021