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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| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
29.10.2022
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2210.16664 |
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| 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. |
|---|---|
| AbstractList | 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. |
| Author | Juditsky, Anatoli Nemirovski, Arkadi |
| Author_xml | – sequence: 1 givenname: Anatoli surname: Juditsky fullname: Juditsky, Anatoli – sequence: 2 givenname: Arkadi surname: Nemirovski fullname: Nemirovski, Arkadi |
| BackLink | https://doi.org/10.48550/arXiv.2210.16664$$DView paper in arXiv |
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| Snippet | The subject of this paper is regularity-preserving aggregation of regular
norms on finite-dimensional linear spaces. Regular norms were introduced in [5]
and... |
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| Title | Aggregating regular norms |
| URI | https://arxiv.org/abs/2210.16664 |
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