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http://hdl.handle.net/10397/106166
Title: | Optimality conditions for nonsmooth nonconvex-nonconcave min-max problems and generative adversarial networks | Authors: | Jiang, J Chen, XJ |
Issue Date: | 2023 | Source: | SIAM journal on mathematics of data science, 2023, v. 5, no. 3, p. 693-722 | 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. | Keywords: | Min-max problem Nonsmooth Nonconvex-nonconcave Optimality condition Generative adversarial networks |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on mathematics of data science | EISSN: | 2577-0187 | DOI: | 10.1137/22M1482238 | Rights: | © 2023 Society for Industrial and Applied Mathematics 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. |
Appears in Collections: | Journal/Magazine Article |
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