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Proximal Methods with Bregman Distances to Solve VIP on Hadamard manifolds

E.A. Papa Quiroz(erikpapa***at***gmail.com)
P.R. Oliveira(poliveir***at***cos.ufrj.br)

Abstract: We present an extension of the proximal point method with Bregman distances to solve Variational Inequality Problems (VIP) on Hadamard manifolds (simply connected finite dimensional Riemannian manifold with nonpositive sectional curvature). Under some natural assumption, as for example, the existence of solutions of the (VIP) and the monotonicity of the multivalued vector field, we prove that the sequence of the iterates given by the method converges to a solution of the problem.

Keywords: Proximal point methods, Hadamard manifolds, Bregman distances, Variational inequality problems, monotone vector field.

Category 1: Global Optimization

Category 2: Global Optimization (Theory )


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Entry Submitted: 12/18/2011
Entry Accepted: 12/21/2011
Entry Last Modified: 12/18/2011

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