Steepest descent method on a Riemannian manifold: the convex case
نویسنده
چکیده
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. M.S.C. 2000: 34C40, 37N40, 37M05, 65J15.
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تاریخ انتشار 2007