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Tikhonov Regularization Methods for Variational Inequality Problems

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  • H. D. Qi

    (Chinese Academy of Sciences)

Abstract

Motivated by the work of Facchinei and Kanzow (Ref. 1) on regularization methods for the nonlinear complementarity problem and the work of Ravindran and Gowda (Ref. 2) for the box variational inequality problem, we study regularization methods for the general variational inequality problem. A sufficient condition is given which guarantees that the union of the solution sets of the regularized problems is nonempty and bounded. It is shown that solutions of the regularized problems form a minimizing sequence of the D-gap function under a mild condition.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:1:d:10.1023_a:1021802830910
    DOI: 10.1023/A:1021802830910
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    References listed on IDEAS

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    1. N. Yamashita & K. Taji & M. Fukushima, 1997. "Unconstrained Optimization Reformulations of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 439-456, March.
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    Cited by:

    1. E. Allevi & A. Gnudi & I. Konnov, 2006. "The Proximal Point Method for Nonmonotone Variational Inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 553-565, July.
    2. Xin Chen & Houduo Qi & Liqun Qi & Kok-Lay Teo, 2004. "Smooth Convex Approximation to the Maximum Eigenvalue Function," Journal of Global Optimization, Springer, vol. 30(2), pages 253-270, November.

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