Iterative Methods for Variational Inequalities

Muhammad Aslam Noor (), Khalida Inayat Noor () and Themistocles M. Rassias ()
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Muhammad Aslam Noor: COMSATS University Islamabad
Khalida Inayat Noor: COMSATS University Islamabad
Themistocles M. Rassias: National Technical University of Athens

A chapter in Differential and Integral Inequalities, 2019, pp 603-618 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-3-030-27407-8_23

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