The maximal monotonicity notion in Banach spaces is extended to Riemannian manifolds of
nonpositive sectional curvature, Hadamard manifolds, and proved to be equivalent to the …

The notion of variational inequalities is extended to Hadamard manifolds and related to
geodesic convex optimization problems. Existence and uniqueness theorems for variational …

The problem of finding the singularities of monotone vectors fields on Hadamard manifolds
will be considered and solved by extending the well-known proximal point algorithm. For …

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 particularclass of manifolds develop an …

We consider variational inequality problems for set-valued vector fields on general
Riemannian manifolds. The existence results of the solution, convexity of the solution set …

Contraction theory is a methodology for assessing the stability of trajectories of a dynamical
system with respect to one another. In this work, we present the fundamental results of …

We establish the existence and uniqueness results for variational inequality problems on
Riemannian manifolds and solve completely the open problem proposed in [SZ Németh …

The relationship between monotonicity and accretivity on Riemannian manifolds is studied
in this paper and both concepts are proved to be equivalent in Hadamard manifolds. As a …

In this paper, we present a new approach to the proximal point method in the Riemannian
context. In particular, without requiring any restrictive assumptions about the sign of the …

In this article, we present the proximal point method for finding minima of a special class of
nonconvex function on a Hadamard manifold. The well definedness of the sequence …