We present an extension of the proximal point method with Bregman distances to solve variational inequality problems (VIP) on Hadamard manifolds with null sectional curvature. Under some natural assumptions, 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. Furthermore, this convergence is linear or superlinear with respect to the Bregman distance.
|Number of pages||25|
|Journal||Journal of the Operations Research Society of China|
|State||Published - Sep 2021|
Bibliographical noteFunding Information:
The authors express their gratitude to professor S.Z. N?meth for sending various papers of his authorship related to vector fields on Riemannian manifolds.
© 2020, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.
- Bregman distances
- Hadamard manifolds
- Monotone vector field
- Proximal point methods
- Variational inequality problems