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Some Proximal Methods for Solving Mixed Variational Inequalities

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  • Muhammad Aslam Noor
  • Zhenyu Huang

Abstract

It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

Suggested Citation

  • Muhammad Aslam Noor & Zhenyu Huang, 2012. "Some Proximal Methods for Solving Mixed Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, May.
    • Handle: RePEc:hin:jnlaaa:610852
    DOI: 10.1155/2012/610852
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    Cited by:

    1. Sorin-Mihai Grad & Felipe Lara, 2021. "Solving Mixed Variational Inequalities Beyond Convexity," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 565-580, August.
    2. Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.

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