Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/106166
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Jiang, J | en_US |
dc.creator | Chen, XJ | en_US |
dc.date.accessioned | 2024-05-03T00:45:34Z | - |
dc.date.available | 2024-05-03T00:45:34Z | - |
dc.identifier.uri | http://hdl.handle.net/10397/106166 | - |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.rights | © 2023 Society for Industrial and Applied Mathematics | en_US |
dc.rights | The following publication Jiang, J., & Chen, X. (2023). Optimality Conditions for Nonsmooth Nonconvex-Nonconcave Min-Max Problems and Generative Adversarial Networks. SIAM Journal on Mathematics of Data Science, 5(3), 693-722 is available at https://dx.doi.org/10.1137/22M1482238. | en_US |
dc.subject | Min-max problem | en_US |
dc.subject | Nonsmooth | en_US |
dc.subject | Nonconvex-nonconcave | en_US |
dc.subject | Optimality condition | en_US |
dc.subject | Generative adversarial networks | en_US |
dc.title | Optimality conditions for nonsmooth nonconvex-nonconcave min-max problems and generative adversarial networks | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 693 | en_US |
dc.identifier.epage | 722 | en_US |
dc.identifier.volume | 5 | en_US |
dc.identifier.issue | 3 | en_US |
dc.identifier.doi | 10.1137/22M1482238 | en_US |
dcterms.abstract | This paper considers a class of nonsmooth nonconvex-nonconcave min-max problems in machine learning and games. We first provide sufficient conditions for the existence of global minimax points and local minimax points. Next, we establish the first-order and second-order optimality conditions for local minimax points by using directional derivatives. These conditions reduce to smooth minmax problems with Fre'\chet derivatives. We apply our theoretical results to generative adversarial networks (GANs) in which two neural networks contest with each other in a game. Examples are used to illustrate applications of the new theory for training GANs. | en_US |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | SIAM journal on mathematics of data science, 2023, v. 5, no. 3, p. 693-722 | en_US |
dcterms.isPartOf | SIAM journal on mathematics of data science | en_US |
dcterms.issued | 2023 | - |
dc.identifier.isi | WOS:001072089700005 | - |
dc.identifier.eissn | 2577-0187 | en_US |
dc.description.validate | 202405 bcrc | en_US |
dc.description.oa | Version of Record | en_US |
dc.identifier.FolderNumber | OA_Scopus/WOS | - |
dc.description.fundingSource | RGC | en_US |
dc.description.fundingSource | Others | en_US |
dc.description.fundingText | Hong Kong Polytechnic University | en_US |
dc.description.pubStatus | Published | en_US |
dc.description.oaCategory | VoR allowed | en_US |
Appears in Collections: | Journal/Magazine Article |
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File | Description | Size | Format | |
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22m1482238.pdf | 502.52 kB | Adobe PDF | View/Open |
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