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Projection Method Approach for General Regularized Non-convex Variational Inequalities

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  • Javad Balooee

    (Sari Branch, Islamic Azad University)

Abstract

In this paper, we investigate or analyze non-convex variational inequalities and general non-convex variational inequalities. Two new classes of non-convex variational inequalities, named regularized non-convex variational inequalities and general regularized non-convex variational inequalities, are introduced, and the equivalence between these two classes of non-convex variational inequalities and the fixed point problems are established. A projection iterative method to approximate the solutions of general regularized non-convex variational inequalities is suggested. Meanwhile, the existence and uniqueness of solution for general regularized non-convex variational inequalities is proved, and the convergence analysis of the proposed iterative algorithm under certain conditions is studied.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:1:d:10.1007_s10957-012-0252-x
    DOI: 10.1007/s10957-012-0252-x
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    References listed on IDEAS

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    1. M. A. Noor, 2010. "On an Implicit Method for Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 411-417, November.
    2. 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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    Cited by:

    1. 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.
    2. Jun Yang & Hongwei Liu, 2018. "A Modified Projected Gradient Method for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 197-211, October.
    3. Javad Balooee & Shih-Sen Chang & Lin Wang & Zhaoli Ma, 2022. "Algorithmic Aspect and Convergence Analysis for System of Generalized Multivalued Variational-like Inequalities," Mathematics, MDPI, vol. 10(12), pages 1-40, June.

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