Geodesic
Convex Compact Sets that Admit a Lower Semicontinuous Strictly Convex Function
Journal of convex analysis, Tome 24 (2017) no. 3, pp. 987-998
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We study the class of compact convex subsets of a topological vector space which admit a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with its weak* topology. In addition, we find many exposed points where a strictly convex lower semicontinuous function is continuous. As a consequence, every set in the above class is the closed convex hull of its exposed points.
Classification : 46A55, 46B03,54E35
Mots-clés : Convex compact set, convex lower semicontinuous function, exposed point, continuity point 
@article{JCA_2017_24_3_JCA_2017_24_3_a14,
     author = {L. C. Garc{\'\i}a-Lirola and J. Orihuela and M. Raja},
     title = {Convex {Compact} {Sets} that {Admit} a {Lower} {Semicontinuous} {Strictly} {Convex} {Function}},
     journal = {Journal of convex analysis},
     pages = {987--998},
     year = {2017},
     volume = {24},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a14/}
}
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L. C. García-Lirola; J. Orihuela; M. Raja. Convex Compact Sets that Admit a Lower Semicontinuous Strictly Convex Function. Journal of convex analysis, Tome 24 (2017) no. 3, pp. 987-998. http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a14/