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Iterative Methods for Variational Inequalities

In: Differential and Integral Inequalities

Author

Listed:
  • Muhammad Aslam Noor

    (COMSATS University Islamabad)

  • Khalida Inayat Noor

    (COMSATS University Islamabad)

  • Themistocles M. Rassias

    (National Technical University of Athens)

Abstract

Variational inequalities can be viewed as novel and significant extension of variational principles. A wide class of unrelated problems, which arise in various branches of pure and applied sciences are being investigated in the unified framework of variational inequalities. It is well known that variational inequalities are equivalent to the fixed point problems. This equivalent fixed point formulation has played not only a crucial part in studying the qualitative behavior of complicated problems, but also provide us numerical techniques for finding the approximate solution of these problems. Our main focus is to suggest some new iterative methods for solving variational inequalities and related optimization problems using projection methods, Wiener–Hopf equations and dynamical systems. Convergence analysis of these methods is investigated under suitable conditions. Some open problems are also discussed and highlighted for future research.

Suggested Citation

  • Muhammad Aslam Noor & Khalida Inayat Noor & Themistocles M. Rassias, 2019. "Iterative Methods for Variational Inequalities," Springer Optimization and Its Applications, in: Dorin Andrica & Themistocles M. Rassias (ed.), Differential and Integral Inequalities, pages 603-618, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-27407-8_23
    DOI: 10.1007/978-3-030-27407-8_23
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