| タイトル |
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en
Dualities for Non-Euclidean Smoothness and Strong Convexity under the Light of Generalized Conjugacy
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| 作成者 |
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Laude, Emanuel
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ORCID 0000-0002-9106-2690
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所属
en
Department of Electrical Engineering (ESAT-STADIUS), KU Leuven
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Themelis, Andreas
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ORCID 0000-0002-6044-0169
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所属
en
Faculty of Information Science and Electrical Engineering (ISEE), Kyushu University
ja
九州大学大学院システム情報科学研究院
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Patrinos, Panagiotis
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ORCID 0000-0003-4824-7697
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所属
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Department of Electrical Engineering (ESAT-STADIUS), KU Leuve
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| アクセス権 |
open access |
| 権利情報 |
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en
© 2022 Society for Industrial and Applied Mathematics
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| 主題 |
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Other
en
Bregman distance
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Other
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eralized conjugacy
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Other
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duality
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Other
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Φ-convexity
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| 内容注記 |
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Abstract
en
Relative smoothness and strong convexity have recently gained considerable attention in optimization. These notions are generalizations of the classical Euclidean notions of smoothness and strong convexity that are known to be dual to each other. However, conjugate dualities for non-Euclidean relative smoothness and strong convexity remain an open problem, as noted earlier by Lu, Freund, and Nesterov [SIAM J. Optim., 28 (2018), pp. 333–354]. In this paper, we address this question by introducing the notions of anisotropic strong convexity and smoothness as the respective dual counterparts. The dualities are developed under the light of generalized conjugacy, which leads us to embed the anticipated dual notions within the superclasses of certain upper and lower envelopes. In contrast to the Euclidean case, these inclusions are proper in general, as showcased by means of counterexamples.
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| 出版者 |
en
Society for Industrial and Applied Mathematics
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| 日付 |
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| 言語 |
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| 資源タイプ |
journal article |
| 出版タイプ |
VoR |
| 資源識別子 |
HDL
https://hdl.handle.net/2324/7151986
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| 関連 |
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isIdenticalTo
DOI
https://doi.org/10.1137/21M1465913
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| 助成情報 |
- 助成機関名
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Research Foundation Flanders (FWO)
- 研究課題番号
G081222N
- 助成機関名
en
Research Foundation Flanders (FWO)
- 研究課題番号
G033822N
- 助成機関名
en
Research Foundation Flanders (FWO)
- 研究課題番号
G0A0920N
- 助成機関名
en
European Union
- 研究課題名
en
Horizon 2020 research
- 助成機関名
en
Marie Skłodowska-Curie
- 研究課題番号
953348
- 研究課題名
en
innovation program
- 助成機関名
en
postdoctoral mandate
- 研究課題番号
PDMt1/22/023
- 助成機関ID
Crossref Funder
https://doi.org/10.13039/501100001691
- 助成機関名
en
Japan Society for the Promotion of Science (JSPS)
ja
日本学術振興会
- 研究課題番号
21K17710
https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-21K17710/
- 研究課題名
en
New-generation optimization algorithms for engineering
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| 収録誌情報 |
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PISSN
1052-6234
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EISSN
1095-7189
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NCID
AA10821632
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en
SIAM Journal on Optimization
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巻33
号4
開始ページ2721
終了ページ2749
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| ファイル |
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| コンテンツ更新日時 |
2024-12-07 |
