Aggregating regular norms

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 probabilit...

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Bibliographic Details
Main Authors Juditsky, Anatoli, Nemirovski, Arkadi
Format Journal Article
LanguageEnglish
Published 29.10.2022
Subjects
Mathematics - Optimization and Control
Online AccessGet full text
DOI10.48550/arxiv.2210.16664

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Summary: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.
DOI:10.48550/arxiv.2210.16664