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Pré-Publication, Document De Travail Année : 2023

Aggregating regular norms

Résumé

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.this http URL], 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.

Dates et versions

hal-03952058 , version 1 (23-01-2023)

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Anatoli B. Juditsky, Arkadi Nemirovski. Aggregating regular norms. 2023. ⟨hal-03952058⟩
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