TITLE

Monotone vector fields and the proximal point algorithm on Hadamard manifolds

AUTHOR(S)
Chong Li; Genaro López; Victoria Martín-Márquez
PUB. DATE
June 2009
SOURCE
Journal of the London Mathematical Society;Jun2009, Vol. 79 Issue 3, p663
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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.
ACCESSION #
39988780

 

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