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Resolvent Algorithms for Mixed Quasivariational Inequalities

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  • M. A. Noor

    (Etisalat College of Engineering)

Abstract

It is well known that mixed quasivariational inequalities are equivalent to implicit resolvent equations. We use this alternative equivalent formulation to suggest and analyze a new modified resolvent method for solving mixed quasivariational inequalities and related problems. We show that the convergence of this modified method requires only pseudomonotonicity, which is a weaker condition than monotonicity. Since mixed quasivariational inequalities include various classes of variational inequalities as special cases, our result continues to hold for these problems.

Suggested Citation

  • M. A. Noor, 2003. "Resolvent Algorithms for Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 137-149, October.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:1:d:10.1023_b:jota.0000005045.32773.37
    DOI: 10.1023/B:JOTA.0000005045.32773.37
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    References listed on IDEAS

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    1. 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.
    2. M.A. Noor, 2002. "Proximal Methods for Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 453-459, November.
    3. M.A. Noor, 2003. "Extragradient Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 475-488, June.
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    Cited by:

    1. N. N. Tam & J. C. Yao & N. D. Yen, 2008. "Solution Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 253-273, August.
    2. M. A. Noor, 2004. "Auxiliary Principle Technique for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 371-386, August.
    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. M. A. Noor, 2004. "Iterative Schemes for Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 385-395, May.

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