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Korpelevich’s method for variational inequality problems on Hadamard manifolds

Listed author(s):
  • Guo-ji Tang
  • Nan-jing Huang


Registered author(s):

    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

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    Article provided by Springer in its journal Journal of Global Optimization.

    Volume (Year): 54 (2012)
    Issue (Month): 3 (November)
    Pages: 493-509

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    Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:493-509
    DOI: 10.1007/s10898-011-9773-3
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    1. Alfredo Iusem & Mostafa Nasri, 2011. "Korpelevich’s method for variational inequality problems in Banach spaces," Journal of Global Optimization, Springer, vol. 50(1), pages 59-76, May.
    2. O. Ferreira & L. Pérez & S. Németh, 2005. "Singularities of Monotone Vector Fields and an Extragradient-type Algorithm," Journal of Global Optimization, Springer, vol. 31(1), pages 133-151, 01.
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