Proximal Point Algorithm On Riemannian Manifolds

By Orizon Pereira Ferreira, P. Oliveira. 2002

378 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/381400ebb55c06c7972d0cda20febe98b6a1f3b5

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Monotone and Accretive Vector Fields on Riemannian Manifolds (2010, methodology): “Moreover, the extension of the maximal monotonicity to the setting of Riemannian manifolds renders feasible the definition of a proximal-type method in order to approximate singularities of set-valued vector fields; see [6, 23, 24].”
Monotone vector fields and the proximal point algorithm on Hadamard manifolds (2009, methodology): “We first recall the notion of Fejér convergence and the following related result (see [12]).”
Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds (2011, neutral): “It was proved in [14] that R f λ is a single-valued mapping with D(R f λ ) = M for each λ > 0, which is characterized by exp−1 yλ x ∈ ∂ f (yλ), ∀x ∈ M, (61)”
The proximal point algorithm in metric spaces (2012, methodology): “In particular, the proximal point algorithm in the context of Riemannian manifold (of nonpositive sectional curvature) was studied in [6, 12, 20, 24].”
ITERATIVE ALGORITHMS FOR NONEXPANSIVE MAPPINGS ON HADAMARD MANIFOLDS (2010, neutral): “[28, 5, 21, 6, 7]).”
Proximal point method for a special class of nonconvex functions on Hadamard manifolds (2008, methodology): “The proximal point algorithm, introduced by Martinet [21] and Rockafellar [27], has been extended to different contexts, see [13], [19], [25] and their references.”
Existence of solutions for variational inequalities on Riemannian manifolds (2009, methodology): “For example, the well-known Kantorovich theorem and the famous Smale point estimate theory for Newton’s method (for solving equations) on Banach spaces were established respectively in [2, 13] and [2, 8, 20] for vector fields on Riemannian manifolds; while the convergence results of the proximal poi”
Proximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifolds (2009, methodology): “Our approach is new but it is related to the work of Ferreira and Oliveira [14].”