Aggregating regular norms
Abstract
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.
Cite
@article{arxiv.2210.16664,
title = {Aggregating regular norms},
author = {Anatoli Juditsky and Arkadi Nemirovski},
journal= {arXiv preprint arXiv:2210.16664},
year = {2024}
}