# Application and issues in abstract convexity

arXiv: https://arxiv.org/abs/2202.09959 · HTML: https://mlsanity.com/paper/2202.09959/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2022.

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

- [Estimating the size of a set using cascading exclusion](https://mlsanity.com/paper/2508.05901/) (2025)

## Abstract (arXiv)

The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this area has not found many practical applications yet. In this paper we study the application of abstract convexity to function approximation. Another important research direction addressed in this paper is the connection with the so-called axiomatic convexity.