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 …

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 …

In this work, we consider monotone Riemannian Variational Inequality Problems (RVIPs),
which encompass both Riemannian convex optimization and minimax optimization as …

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 …

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 …

In this paper, we study the Karush–Kuhn–Tucker optimality conditions in an optimization
problem with interval-valued objective function on Hadamard manifolds. The gH-directional …

In this article, we introduce a forward–backward splitting method with a new step size rule for
finding a singularity point of an inclusion problem which is defined by means of a sum of 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 …