# Aggregating regular norms

arXiv: https://arxiv.org/abs/2210.16664 · HTML: https://mlsanity.com/paper/2210.16664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2022.

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

- [Solving Stochastic Fixed-Point Equations with High Probability](https://mlsanity.com/paper/2607.09097/) (2026)

## Abstract (arXiv)

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in 1) high-dimensional convex geometry and probability in Banach spaces [0.9.12.13.15], and in 2) design of proximal first-order algorithms for large-scale convex optimization with dimension-independent, or nearly so, complexity. Regularity, with moderate parameters, of a norm makes applicable, in a dimension-independent fashion, numerous geometric, probabilistic, and optimization-related results, which motivates our interest in aggregating regular norms with controlled (and moderate) inflation of regularity parameters.