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Parametric Extended General Mixed Variational Inequalities

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  • Muhammad Aslam Noor

Abstract

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational inequalities, quasi (mixed) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. In fact, our results can be considered as a significant extension of previously known results.

Suggested Citation

  • Muhammad Aslam Noor, 2012. "Parametric Extended General Mixed Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:201947
    DOI: 10.1155/2012/201947
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    References listed on IDEAS

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    1. Jerzy Kyparisis, 1990. "Sensitivity Analysis for Nonlinear Programs and Variational Inequalities with Nonunique Multipliers," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 286-298, May.
    2. M. A. Noor, 1997. "Sensitivity Analysis for Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 399-407, November.
    3. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, March.
    4. Yuping Qiu & Thomas L. Magnanti, 1989. "Sensitivity Analysis for Variational Inequalities Defined on Polyhedral Sets," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 410-432, August.
    5. Muhammad Aslam Noor & Khalida Inayat Noor & Zhenyu Huang & Eisa Al-Said, 2012. "Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, January.
    6. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Abdellatif Moudafi & Muhammad Aslam Noor, 1999. "Sensitivity analysis for variational inclusions by Wiener-Hopf equation techniques," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-10, January.
    8. Stella Dafermos, 1988. "Sensitivity Analysis in Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 421-434, August.
    9. Muhammad Aslam Noor & Khalida Inayat Noor & Zhenyu Huang & Eisa Al-Said, 2012. "Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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