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Regularized Nonconvex Mixed Variational Inequalities: Auxiliary Principle Technique and Iterative Methods

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  • Javad Balooee

    (Islamic Azad University)

Abstract

In this paper, we turn our attention to formulating and studying a new class of variational inequalities in a nonconvex setting, called regularized nonconvex mixed variational inequalities. By using the auxiliary principle technique, some new predictor corrector methods for solving such class of regularized nonconvex mixed variational inequalities are suggested and analyzed. The study of convergence analysis of the proposed iterative algorithms requires either pseudomonotonicity or partially mixed relaxed and strong monotonicity of the operator involved in regularized nonconvex mixed variational inequalities. As a consequence of our main results, we provide the correct versions of the algorithms and results presented in the literature.

Suggested Citation

  • Javad Balooee, 2017. "Regularized Nonconvex Mixed Variational Inequalities: Auxiliary Principle Technique and Iterative Methods," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 774-801, March.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-016-1046-3
    DOI: 10.1007/s10957-016-1046-3
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    References listed on IDEAS

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    1. M.A. Noor, 2002. "Proximal Methods for Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 447-452, November.
    2. Qamrul Hasan Ansari & Javad Balooee, 2013. "Predictor–Corrector Methods for General Regularized Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 473-488, November.
    3. Javad Balooee, 2013. "Projection Method Approach for General Regularized Non-convex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 192-209, October.
    4. M.A. Noor, 2002. "Proximal Methods for Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 453-459, November.
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