Proximal Methods with Bregman Distances to Solve VIP on Hadamard manifolds

Published: 2011/12/18

Global Optimization, Global Optimization Theory bregman distances, hadamard manifolds, monotone vector field, proximal point algorithm, variational inequality Short URL: https://optimization-online.org/?p=11855

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.

Proximal Methods with Bregman Distances to Solve VIP on Hadamard manifolds

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