Singularities of monotone vector fields and an extragradient-type algorithm

Abstract. Bearing in mind the notion of monotone vector field on Riemannian manifolds, see [12–16], we study the set of their singularities and for a particular class of manifolds develop an extragradient-type algorithm convergent to singularities of such vector fields. In particular, our method can be used for solving nonlinear constrained optimization problems in Euclidean space, with a convex objective function and the constraint set a constant curvature Hadamard manifold. Our paper shows how tools of convex analysis on Riemannian manifolds can be used to solve some nonconvex constrained problem in a Euclidean space