Geodesic
About the Existence of an Isotone Retraction onto a Convex Cone
Journal of convex analysis, Tome 18 (2011) no. 3, pp. 707-72.

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

The existence of continuous isotone retractions onto pointed closed convex cones in Hilbert spaces is studied. The cones admitting such mappings are called isotone retraction cones. In finite dimension, generating, isotone retraction cones are polyhedral. For a closed, pointed, generating cone in a Hilbert space the isotonicity of a retraction and its complement implies that the cone is latticial and the retraction is well defined by the latticial structure. The notion of sharp mapping is introduced. If the cone is generating and normal, it is proved that its latticiality is equivalent to the existence of an isotone retraction onto it, whose complement is sharp. The subdual and autodual latticial cones are also characterized by isotonicity. This is done by attempting to extend Moreau's theorem to retractions. 
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     author = {S. Z. N\'emeth and A. B. N\'emeth},
     title = {About the {Existence} of an {Isotone} {Retraction} onto a {Convex} {Cone}},
     journal = {Journal of convex analysis},
     pages = {707--72},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a7/}
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S. Z. Németh; A. B. Németh. About the Existence of an Isotone Retraction onto a Convex Cone. Journal of convex analysis, Tome 18 (2011) no. 3, pp. 707-72. http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a7/