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Some iterative methods for nonconvex variational inequalities

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It is well known that the nonconvex variational inequalities are equivalent to the fixed point problems. We use this equivalent alternative formulation to suggest and analyze a new class of two-step iterative methods for solving the nonconvex variational inequalities. We discuss the convergence of the iterative method under suitable conditions. We also introduce a new class of Wiener – Hopf equations. We establish the equivalence between the nonconvex variational inequalities and the Wiener – Hopf equations. This alternative equivalent formulation is used to suggest some iterative methods. We also consider the convergence analysis of these iterative methods. Our method of proofs is very simple compared to other techniques.

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  1. Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

    Muhammad Aslam Noor

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  1. Muhammad Aslam Noor
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Aslam Noor, M. Some iterative methods for nonconvex variational inequalities. Comput Math Model 21, 97–108 (2010). https://doi.org/10.1007/s10598-010-9057-7

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