TITLE

Steepest descent method on a Riemannian manifold: the convex case

AUTHOR(S)
Munier, Julien
PUB. DATE
July 2007
SOURCE
Balkan Journal of Geometry & Its Applications;2007, Vol. 12 Issue 2, p98
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper we are interested in the asymptotic behavior of the trajectories of the famous steepest descent evolution equation on Riemannian manifolds. It writes ẋ (t) + gradϕ (x (t)) = 0. It is shown how the convexity of the objective function ϕ helps in establishing the convergence as time goes to infinity of the trajectories towards points that minimize ϕ. Some numerical illustrations are given for the Rosenbrock's function.
ACCESSION #
27694378

 

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