Geodesic
On the Infimum of a Quasiconvex Function over an Intersection. Application to the Distance Function
Journal of convex analysis, Tome 18 (2011) no. 3, pp. 687-698.

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

We give sufficient conditions for the infimum of a quasiconvex function $f$ over the intersection $\bigcap_{i\in I}R_{i}$ to agree with the supremum of the infima of $f$ over the $R_{i}$'s. We apply these results to the distance function in a normed space.
Classification : 54E35, 26-99
Mots-clés : Quasiconvex functions, distance to the intersection 
@article{JCA_2011_18_3_JCA_2011_18_3_a5,
     author = {J.-E. Mart{\'\i}nez Legaz and A. Martin\'on},
     title = {On the {Infimum} of a {Quasiconvex} {Function} over an {Intersection.} {Application} to the {Distance} {Function}},
     journal = {Journal of convex analysis},
     pages = {687--698},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a5/}
}
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J.-E. Martínez Legaz; A. Martinón. On the Infimum of a Quasiconvex Function over an Intersection. Application to the Distance Function. Journal of convex analysis, Tome 18 (2011) no. 3, pp. 687-698. http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a5/