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Iterative Methods for General 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 fixed-point problems. We use this alternative equivalent formulation to suggest and analyze a new self-adaptive resolvent method for solving mixed quasivariational inequalities in conjunction with a technique updating the solution. We show that the convergence of this method requires pseudomonotonicity, which is a weaker condition than monotonicity. Since mixed quasivariational inequalities include various classes of variational inequalities as special cases, our results continue to hold for these problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:1:d:10.1023_b:jota.0000005044.11591.bd
    DOI: 10.1023/B:JOTA.0000005044.11591.bd
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    References listed on IDEAS

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    1. M.A. Noor, 2003. "Extragradient Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 475-488, June.
    2. 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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    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. 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.
    3. M. A. Noor, 2004. "Iterative Schemes for Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 385-395, May.
    4. 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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