Monotone point-to-set vector fields.

By J. C. Neto, Orizon Pereira Ferreira, L. R. L. Pérez. 2000

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Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds (2011, unknown): “Definition 2 [9, 10, 28, 32] A vector field A ∈ X (M) is said to be (a) monotone if for any x, y ∈ D(A) 〈 u, exp−1 x y 〉 ≤ v,− exp−1 y x 〉 , ∀u ∈ A(x) and ∀v ∈ A(y); (30) (b) strongly monotone if there exists ρ > 0 such that for any x, y ∈ D(A), 〈 u, exp−1 x y 〉 − v, − exp−1 y x 〉 ≤ −ρd2(x, y), ∀u ∈”
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”
Monotone vector fields and the proximal point algorithm on Hadamard manifolds (2009, background): “In particular, the notion of monotone vector fields on Hadamard manifolds was introduced by Németh [20] and extended by Da Cruz Neto, Ferreira and Lucambio Pérez [8] to the case of multivalued vector fields.”