Aggregating regular norms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911774351032320 |
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| author | Juditsky, Anatoli Nemirovski, Arkadi |
| author_facet | Juditsky, Anatoli Nemirovski, Arkadi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_16664 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Aggregating regular norms Juditsky, Anatoli Nemirovski, Arkadi Optimization and Control 52A21, 90C06, 90C25 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. |
| title | Aggregating regular norms |
| topic | Optimization and Control 52A21, 90C06, 90C25 |
| url | https://arxiv.org/abs/2210.16664 |