Geodesic
Separation Properties in some Idempotent and Symmetrical Convex Structure
Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1143-1168
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B-convexity was defined by the author and C. D. Horvath [B-convexity, Optimization 53(2) (2004) 103--127] as a suitable Kuratowski-Painlevé upper limit of linear convexities over a finite dimensional Euclidean vector space. Recently, an alternative formulation over the whole Euclidean vector space was proposed [W. Briec, Some remarks on an idempotent and non-associative convex structure, Journal of Convex Analysis 22 (2015) 259--289]. In this paper a convex separation framework is proposed as well as some extension of known results established over posets. We first analyze the algebraic properties of some class of subsets characterized by a suitable notion of dual form. Along this line some extended separation results are established by considering the Kuratowski-Painlevé limit of a sequence of linear halfspaces.
Classification : 06D50, 32F17
Mots-clés : Idempotence, semilattices, generalized convexity, B-convexity 
@article{JCA_2017_24_4_JCA_2017_24_4_a4,
     author = {W. Briec},
     title = {Separation {Properties} in some {Idempotent} and {Symmetrical} {Convex} {Structure}},
     journal = {Journal of convex analysis},
     pages = {1143--1168},
     year = {2017},
     volume = {24},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a4/}
}
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W. Briec. Separation Properties in some Idempotent and Symmetrical Convex Structure. Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1143-1168. http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a4/