Weakly Upward-Downward Minimax Theorem

Cheng, Cao-Zong; Lin, Bor-Luh; Yu, Feng-Shuo

doi:10.1007/978-94-015-9113-3_2

Cao-Zong Cheng⁵,
Bor-Luh Lin⁶ &
Feng-Shuo Yu⁶

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 26))

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Abstract

Let X and Y be nonempty sets and let f be a real-valued function defined on X × Y. For S ⊂ X and T ⊂ Y, let

$$ {f^*}(S,T) = \mathop {\inf }\limits_T \mathop {sup}\limits_S f(x,y),{f_*}(S,T) = \mathop {sup}\limits_S \mathop {\inf }\limits_T f(x,y)$$

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Author information

Authors and Affiliations

Department of Mathematics Computer Institute, Beijing Polytechnic University, Beijing, 100044, China
Cao-Zong Cheng
Department of Mathemtics, University of Iowa, Iowa City, IA, 52242, USA
Bor-Luh Lin & Feng-Shuo Yu

Authors

Cao-Zong Cheng
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Bor-Luh Lin
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Feng-Shuo Yu
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Editor information

Editors and Affiliations

Department of Mathematics, University of Catania, Catania, Italy
Biagio Ricceri
Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California, USA
Stephen Simons

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Cheng, CZ., Lin, BL., Yu, FS. (1998). Weakly Upward-Downward Minimax Theorem. In: Ricceri, B., Simons, S. (eds) Minimax Theory and Applications. Nonconvex Optimization and Its Applications, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9113-3_2

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DOI: https://doi.org/10.1007/978-94-015-9113-3_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5030-4
Online ISBN: 978-94-015-9113-3
eBook Packages: Springer Book Archive

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