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Extragradient Methods for Pseudomonotone Variational Inequalities

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  • M.A. Noor

    (Etisalat College of Engineering)

Abstract

We consider and analyze some new extragradient-type methods for solving variational inequalities. The modified methods converge for a pseudomonotone operator, which is a much weaker condition than monotonicity. These new iterative methods include the projection, extragradient, and proximal methods as special cases. Our proof of convergence is very simple as compared with other methods.

Suggested Citation

  • M.A. Noor, 2003. "Extragradient Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 475-488, June.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:3:d:10.1023_a:1023989403613
    DOI: 10.1023/A:1023989403613
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    References listed on IDEAS

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    1. M. A. Noor & E. A. Al-Said, 1999. "Wiener–Hopf Equations Technique for Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 705-714, December.
    2. B. S. He & L. Z. Liao, 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 111-128, January.
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    Cited by:

    1. M. A. Noor, 2004. "Auxiliary Principle Technique for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 371-386, August.
    2. Trinh Ngoc Hai, 2020. "Two modified extragradient algorithms for solving variational inequalities," Journal of Global Optimization, Springer, vol. 78(1), pages 91-106, September.
    3. M. A. Noor, 2003. "Iterative Methods for General Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 123-136, October.
    4. M. A. Noor & K. I. Noor, 2004. "On General Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 579-599, March.
    5. Chinedu Izuchukwu & Yekini Shehu & Jen-Chih Yao, 2022. "New inertial forward-backward type for variational inequalities with Quasi-monotonicity," Journal of Global Optimization, Springer, vol. 84(2), pages 441-464, October.
    6. M. A. Noor, 2004. "Iterative Schemes for Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 385-395, May.
    7. M. A. Noor, 2003. "Resolvent Algorithms for Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 137-149, October.

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