Journal of Optimization Theory and Applications

, Volume 102, Issue 1, pp 193-201

Tikhonov Regularization Methods for Variational Inequality Problems

  • H. D. QiAffiliated withInstitute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences

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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.

Variational inequality problems regularization methods minimizing sequences