Tseng's extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds

ABSTRACT

In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.

Keywords:

• Pseudomonotone vector field
• variational inequality
• extragradient algorithm
• non-Lipschitzian
• Hadamard manifold

2010 Mathematics Subject Classifications:

• 47H05
• 47H09

Disclosure statement

No potential conflict of interest was reported by the author(s).