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 …

An equilibrium theory is developed in Hadamard manifolds. The existence of equilibrium
points for a bifunction is proved under suitable conditions, and applications to variational …

Firmly nonexpansive mappings play an important role in metric fixed point theory and
optimization due to their correspondence with maximal monotone operators. In this paper …

From optimal transport to robust dimensionality reduction, many machine learning
applicationscan be cast into the min-max optimization problems over Riemannian manifolds …

This is the first paper dealing with the study of weak sharp minima for constrained
optimization problems on Riemannian manifolds, which are important in many applications …

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 …

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 the paper, we study a class of useful minimax problems on Riemanian manifolds and
propose a class of effective Riemanian gradient-based methods to solve these minimax …

Firmly nonexpansive mappings are introduced in Hadamard manifolds, a particular class of
Riemannian manifolds with nonpositive sectional curvature. The resolvent of a set-valued …