Korpelevich’s method for variational inequality problems on Hadamard manifolds

Guo-ji Tang and Nan-jing Huang ()

Journal of Global Optimization, 2012, vol. 54, issue 3, 493-509

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. Copyright Springer Science+Business Media, LLC. 2012

Keywords: Extragradient method; Variational inequality; Hadamardmanifold; Pseudomonotone vector field; 49J40; 47J25; 47H05 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-011-9773-3

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