Geodesic
Minimax Equalities by Reconstruction of Polytopes
Journal of convex analysis, Tome 7 (2000) no. 2, pp. 335-352.

Voir la notice de l'article provenant de la source Heldermann Verlag

Given a quasi-concave-convex real-valued function f: X×Y --> R defined on the product of two convex sets we would like to know if inffY supX f = supX inffY f. We showed in another paper [A reconstruction of polytopes by convex pastings, to appear in Mathematika] that this question is very closely related to the following "reconstruction" problem: given a polytope (i.e. the convex hull of a finite set of points) X and a family F of subpolytopes of X, we would like to know if X is an element of F, knowing that any polytope which is obtained by cutting an element of F with a hyperplane or by pasting two elements of F along a common facet is also in F. Here, we consider a similar reconstruction problem for arbitrary convex sets. 
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     author = {G. H. Greco and Ch. D. Horvath},
     title = {Minimax {Equalities} by {Reconstruction} of {Polytopes}},
     journal = {Journal of convex analysis},
     pages = {335--352},
     publisher = {mathdoc},
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     number = {2},
     year = {2000},
     url = {http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a5/}
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G. H. Greco; Ch. D. Horvath. Minimax Equalities by Reconstruction of Polytopes. Journal of convex analysis, Tome 7 (2000) no. 2, pp. 335-352. http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a5/