Abstract
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.
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Tang, Gj., Huang, Nj. Korpelevich’s method for variational inequality problems on Hadamard manifolds. J Glob Optim 54, 493–509 (2012). https://doi.org/10.1007/s10898-011-9773-3
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DOI: https://doi.org/10.1007/s10898-011-9773-3