# An Extragradient-type Algorithm for Variational Inequality on Hadamard Manifolds

arXiv: https://arxiv.org/abs/1804.09292 · HTML: https://mlsanity.com/paper/1804.09292/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties](https://mlsanity.com/paper/2305.16186/) (2023)

## Abstract (arXiv)

The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of ε-enlargement of maximal monotone vector fields is used and its lower-semicontinuity is stablished in order to obtain the convergence of the method in this new context.