Steepest descent method on a Riemannian manifold: the convex case

Julien Munier (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We are interested in the asymptotic behavior of the trajectories of the famous steepest descent evolution equation on Riemannian manifolds. It is shown how the convexity of the objective function helps in establishing the convergence as time goes to infinity of the trajectories towards points that minimize that function. Some numerical illustrations are given for Rosenbrock's function.

Domaines: Optimisation et contrôle [math.OC]

Julien Munier. Steepest descent method on a Riemannian manifold: the convex case. 2006. ⟨hal-00018758⟩