Geodesic
On Minimax Theorems for Lower Semicontinuous Functions in Hilbert Spaces
Journal of convex analysis, Tome 25 (2018) no. 2, pp. 389-402
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We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tools are the theory of Φ-convex functions and sufficient and necessary conditions for the minimax equality for general Φ-convex functions. The conditions we propose are expressed in terms of abstract Φ-subgradients.
Classification : 32F17, 49J52, 49K27, 49K35, 52A01
Mots-clés : Abstract convexity, minimax theorems, intersection property, abstract Phi-subdifferential, abstract Phi-subgradient 
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     author = {E. Bednarczuk and M. Syga},
     title = {On {Minimax} {Theorems} for {Lower} {Semicontinuous} {Functions} in {Hilbert} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {389--402},
     year = {2018},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a3/}
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E. Bednarczuk; M. Syga. On Minimax Theorems for Lower Semicontinuous Functions in Hilbert Spaces. Journal of convex analysis, Tome 25 (2018) no. 2, pp. 389-402. http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a3/