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Iterative Methods for Variational Inequalities

  • Muhammad Aslam Noor
  • Khalida Inayat Noor
  • Themistocles M. Rassias
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 151)

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.

Notes

Acknowledgements

Authors would like to express their sincere gratitude to Prof. Dr. Abdellah Bnohachem for providing the computational results.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Muhammad Aslam Noor
    • 1
  • Khalida Inayat Noor
    • 1
  • Themistocles M. Rassias
    • 2
  1. 1.COMSATS University IslamabadIslamabadPakistan
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece

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