The Proximal Point Algorithm in Riemannian Manifolds
O. P. Ferreira and Oliveira, P. R.
In this paper we consider the minimization problem with
constraints. We will show that if the set of constraints is a
Riemannian manifold of nonpositive sectional curvature, and the
objective function is convex in this manifold, then the proximal point
method in Euclidean space is naturally extended to solve minimization
problems in Riemannian manifolds. We will prove that the sequence
generated by our method is well defined and converges to a minimizer
point. In particular we show how tools of Riemannian geometry, more
specifically the convex analysis in Riemannian manifolds, can be used
to solve nonconvex constrained problems in Euclidean spaces.
T. R. ES-453
Federal University of Rio de Janeiro
09/97, revised 10/99