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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 67, 2018 - Issue 1
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Original Articles

Extragradient method for solving quasivariational inequalities

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Pages 103-112 | Received 12 Jan 2017, Accepted 16 Sep 2017, Published online: 06 Oct 2017

References

  • Bensoussan A, Goursat M, Lions JL. Contrôle impulsionnel et inéquations quasi-variationnelles. C R Acad Sci Paris Ser A. 1973;276:1284–1973.
  • Baiocchi A, Capelo A. Variational and quasi-variational inequalities. New York (NY): Wiley; 1984.
  • Mosco U. Implicit variational problems and quasi variational inequalities. Lecture Notes in \ Math. Vol. 543; 1976. p. 83–156.
  • Bliemer M, Bovy P. Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem. Transportation Research Part B: Methodological. 2003;37:501–519.
  • Harker PT. Generalized Nash games and quasivariational inequalities. Eur J Oper Res. 1991;54:81–94.
  • Kocvara M, Outrata JV. On a class of quasi-variational inequalities. Optim Methods Softw. 1995;5:275–295.
  • Pang JS, Fukushima M. Quasi-variational inequalities, generalized Nash equilibria and Multi-leader-follower games. Comput Manage Sci. 2005;1:21–56.
  • Antipin AS, Jacimovic M, Mijajlovic N. A second-order continuous method for solving quasi-variational inequalities. Comp Math Math Phys. 2011;51(11):1856–1863.
  • Antipin AS, Jaćimović M, Mijajlović N. A second-order iterative method for solving quasi-variational inequalities. Comp Math Math Phys. 2013;53(3):258–264.
  • Mijajlović N, Jaćimović M. Proximal methods for solving quasi-variational inequalities. Comput Math Math Phys. 2015;55(12):1981–1985.
  • Noor MA, Noor KI, Khan AG. Three step iterative algorithms for solving class of quasi variational inequalities. Afrika Math. 2015;26(7):1519–1530.
  • Khan AA, Tammer C, Zalinescu C. Regularization of quasi-variational inequalities. Optimization. 2015;64(8):1703–1724.
  • Korpelevich GM. The extragradient method for finding saddle points and other problems. Matecon. 1976;12:747–756.
  • Antipin AS. Gradient and extragradient approaches to bilinear equilibrium programming. Comput Center RAS. 2002;3(11):2592–2605.
  • Antipin AS, Vasiliev FP. The regularized extragradient method for solving variational inequalities. Comp M Prog. 2002;3(2):144–150.
  • Censor Y, Gibali A, Reich S. Extensions of Korpelevich’s extragradient method for the variational inequality problem in Euclidean space. Optimization. 2012;61:1119–1132.
  • Noor MA. New extragradient-type methods for general variational inequalities. J Math Anal Appl. 2003;277:379–394.
  • Yao Y, Marino G, Muglia L. A modified Korpelevich’s method convergent to the minimum norm solution of a variational inequality. Optimization. 2014;63(4):559–569.
  • Zykina AV, Melen’chuk NV. A two-step extragradient method for variational inequalities. Russ Math. 2010:71–73.
  • Noor MA, Noor KI, Al-Said E, Moudafi A. Some extra-gradient methods for nonconvex quasi-variational inequlities. Bull Math Anal Appl. 2011;3:178–187.
  • Vasiliev FP. Methods of optimization. Moscow: Factorial press; 2002.
  • Noor MA, Oettli W. On general nonlinear complementarity problems and quasi equilibria. Le Math. 1994;49:313–331.
  • Nesterov Yu, Scrimali L. Solving strongly monotone variational and quasi-variational inequalities. Discrete Contin Dyn Syst. 2011;31(4):1383–1396.
  • Noor MA. An iterative scheme for a class of quasi-variational inequalities. J Math Anal Appl. 1985;110:463–468.
  • Ryazantseva IP. First-order methods for certain quasi-variational inequalities in a Hilbert space. Comput Math Math Phys. 2007;47:183–190.

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