Article ID: | iaor20126409 |
Volume: | 54 |
Issue: | 3 |
Start Page Number: | 493 |
End Page Number: | 509 |
Publication Date: | Nov 2012 |
Journal: | Journal of Global Optimization |
Authors: | Huang Nan-jing, Tang Guo-ji |
Keywords: | calculus of variations |
The concept of pseudomonotone vector field on Hadamard manifold is introduced. A variant of Korpelevich’s method for solving the variational inequality problem is extended from Euclidean spaces to constant curvature Hadamard manifolds. Under a pseudomonotone assumption on the underlying vector field, we prove that the sequence generated by the method converges to a solution of variational inequality, whenever it exists. Moreover, we give an example to show the effectiveness of our method.