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The Tikhonov Regularization Method for Set‐Valued Variational Inequalities

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  • Yiran He

Abstract

This paper aims to establish the Tikhonov regularization theory for set‐valued variational inequalities. For this purpose, we firstly prove a very general existence result for set‐valued variational inequalities, provided that the mapping involved has the so‐called variational inequality property and satisfies a rather weak coercivity condition. The result on the Tikhonov regularization improves some known results proved for single‐valued mapping.

Suggested Citation

  • Yiran He, 2012. "The Tikhonov Regularization Method for Set‐Valued Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:172061
    DOI: 10.1155/2012/172061
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    References listed on IDEAS

    as
    1. H. D. Qi, 1999. "Tikhonov Regularization Methods for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 193-201, July.
    2. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, March.
    3. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. I. V. Konnov, 1998. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 165-181, October.
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