Existence of solutions for variational inequalities on Riemannian manifolds

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Proximal point method for a special class of nonconvex functions on Hadamard manifolds (2008, background): “The extension of the concepts and techniques of the Mathematical Programming from Euclidean space to Riemannian manifolds occurs naturally and has been frequently done in recent years, with a theoretical purpose as well as to obtain effective algorithms; see [1], [2], [4], [10], [12], [13], [18], [1”
Monotone and Accretive Vector Fields on Riemannian Manifolds (2010, background): “Keywords Hadamard manifold · Monotone vector field · Accretive vector field · Singularity · Fixed point · Iterative algorithm · Convex function”
Concepts and techniques of optimization on the sphere (2014, background): “The next proposition was first proved in a more general setting in [16] (see also [15]).”
Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds (2011, background): “The study of accretive and monotone type operators in metric spaces has been the focus of many authors in the last decades; see, for example, [10, 12, 13, 22, 23, 27, 28, 30, 32, 34, 40, 44].”
Nonsmooth variational inequalities on Hadamard manifolds (2018, background): “[2] considered variational inequalities in the setting of Riemannian manifolds and proved some existence results for their solutions.”