Geodesic
Direction of Movement of the Element of Minimal Norm in a Moving Convex Set
Journal of convex analysis, Tome 14 (2007) no. 3, pp. 455-463.

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

We show that if $K$ is a nonempty closed convex subset of a real Hilbert space $H$, $e$ is a non-zero arbitrary vector in $H$ and for each $t\in \mathbb{R}$, $z(t)$ is the closest point in $K + te$ to the origin, then the angle $z(t)$ makes with $e$ is a decreasing function of $t$ while $z(t)\neq 0$, and the inner product of $z(t)$ with $e$ is increasing.
Classification : 46C05, 47H99, 41A65
Mots-clés : Moving convex set, nearest point projection 
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     author = {R. Choudhary},
     title = {Direction of {Movement} of the {Element} of {Minimal} {Norm} in a {Moving} {Convex} {Set}},
     journal = {Journal of convex analysis},
     pages = {455--463},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a0/}
}
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R. Choudhary. Direction of Movement of the Element of Minimal Norm in a Moving Convex Set. Journal of convex analysis, Tome 14 (2007) no. 3, pp. 455-463. http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a0/