Details

Autor(en) / Beteiligte

• Li, Chong
• López, Genaro
• Martín-Márquez, Victoria

Titel

Monotone vector fields and the proximal point algorithm on Hadamard manifolds

Ist Teil von

• Journal of the London Mathematical Society, 2009-06, Vol.79 (3), p.663-683

Ort / Verlag

Oxford University Press

Erscheinungsjahr

2009

Quelle

Wiley Online Library

Beschreibungen/Notizen

• 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 upper semicontinuity. We consider the problem of finding a singularity of a multivalued vector field in a Hadamard manifold and present a general proximal point method to solve that problem, which extends the known proximal point algorithm in Euclidean spaces. We prove that the sequence generated by our method is well defined and converges to a singularity of a maximal monotone vector field, whenever it exists. Applications in minimization problems with constraints, minimax problems and variational inequality problems, within the framework of Hadamard manifolds, are presented.