Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds. Issue 12 (10th September 2021) - Chen, Junfeng; Liu, Sanyang; Chang, Xiaokai
ABSTRACT: This paper is devoted to two efficient algorithms for solving variational inequality on Hadamard manifolds. The algorithms are inspired by Tseng's extragradient methods with new step sizes, established without the knowledge of the Lipschitz constant of the mapping. Under a pseudomonotone assumption on the underlying vector field, we prove that the sequence generated by the methods converges to a solution of variational inequality, whenever it exists.