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Iterative Schemes for Nonconvex Variational Inequalities

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  • M. A. Noor

    (Etisalat College of Engineering)

Abstract

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets.

Suggested Citation

  • M. A. Noor, 2004. "Iterative Schemes for Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 385-395, May.
    • Handle: RePEc:spr:joptap:v:121:y:2004:i:2:d:10.1023_b:jota.0000037410.46182.e2
    DOI: 10.1023/B:JOTA.0000037410.46182.e2
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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. "Iterative Methods for General Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 123-136, October.
    3. 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, 2009. "Implicit Iterative Methods for Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 619-624, December.

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