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Iterative Methods for General Mixed Quasivariational Inequalities

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Abstract

It is well known that mixed quasivariational inequalities are equivalent to implicit fixed-point problems. We use this alternative equivalent formulation to suggest and analyze a new self-adaptive resolvent method for solving mixed quasivariational inequalities in conjunction with a technique updating the solution. We show that the convergence of this method requires pseudomonotonicity, which is a weaker condition than monotonicity. Since mixed quasivariational inequalities include various classes of variational inequalities as special cases, our results continue to hold for these problems.

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Authors and Affiliations

  1. Etisalat College of Engineering, Sharjah, United Arab Emirates

    M. A. Noor (Professor)

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  1. M. A. Noor
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Noor, M.A. Iterative Methods for General Mixed Quasivariational Inequalities. Journal of Optimization Theory and Applications 119, 123–136 (2003). https://doi.org/10.1023/B:JOTA.0000005044.11591.bd

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  • DOI: https://doi.org/10.1023/B:JOTA.0000005044.11591.bd

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