# Convex optimization on Banach Spaces

arXiv: https://arxiv.org/abs/1401.0334 · HTML: https://mlsanity.com/paper/1401.0334/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2014.

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

- [Risk Bounds for Mixture Density Estimation on Compact Domains via the h-Lifted Kullback--Leibler Divergence](https://mlsanity.com/paper/2404.12586/) (2024)

## Abstract (arXiv)

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space X. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper bounds for the convergence rate of the proposed algorithms are given. These bounds depend on the smoothness of the objective function and the sparsity or compressibility (with respect to a given dictionary) of a point in X where the minimum is attained.