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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 61, 2012 - Issue 9
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Original Articles

Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space

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Pages 1119-1132 | Received 10 Aug 2010, Accepted 08 Nov 2010, Published online: 21 Dec 2010

References

  • Attouch , H . 1984 . Variational Convergence for Functions and Operators , London : Pitman .
  • Censor , Y , Gibali , A and Reich , S . 2011 . The subgradient extragradient method for solving variational inequalities in Hilbert space . J. Optim. Theory Appl. , 148
  • Facchinei , F and Pang , JS . 2003 . Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols I and II , New York, NY , , USA : Springer-Verlag .
  • Hiriart-Urruty , J-B and Lemaréchal , C . 2001 . Fundamentals of Convex Analysis , Berlin, Heidelberg , , Germany : Springer-Verlag .
  • Iiduka , H , Takahashi , W and Toyoda , M . 2004 . Approximation of solutions of variational inequalities for monotone mappings . PanAm. Math. J. , 14 : 49 – 61 .
  • Israel , MM Jr and Reich , S . 1983 . Extension and selection problems for non-linear semigroups in Banach Spaces . Math. Jpn. , 28 : 1 – 8 .
  • Iusem , AN and Svaiter , BF . 1997 . A variant of Korpelevich's method for variational inequalities with a new search strategy . Optimization , 42 : 309 – 321 .
  • Khobotov , EN . 1989 . Modification of the extra-gradient method for solving variational inequalities and certain optimization problems . USSR Comput. Math. Math. Phys. , 27 : 120 – 127 .
  • Kirszbraun , MD . 1934 . Über die zusammenziehende und Lipschitzsche transformationen . Fund. Math. , 22 : 77 – 108 .
  • Korpelevich , GM . 1976 . The extragradient method for finding saddle points and other problems . Ekon. Mat. Metody , 12 : 747 – 756 .
  • Noor , MA . 1999 . Some algorithms for general monotone mixed variational inequalities . Math. Comput. Model. , 29 : 1 – 9 .
  • Noor , MA . 2004 . Some development in general variational inequalities . Appl. Math. Comput. , 152 : 199 – 277 .
  • Santos , PSM and Scheimberg , S . 2006 . A projection algorithm for general variational inequalities with perturbed constraint set . Appl. Math. Comput. , 181 : 649 – 661 .
  • Solodov , MV and Svaiter , BF . 1999 . A new projection method for variational inequality problems . SIAM J. Control Optim. , 37 : 765 – 776 .
  • Yang , Q and Zhao , J . 2006 . Generalized KM theorems and their applications . Inverse Prob. , 22 : 833 – 844 .

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