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Zbl 0939.90019
Qi, H.D.
Tikhonov regularization methods for variational inequality problems. (English)
[J] J. Optimization Theory Appl. 102, No.1, 193-201 (1999). ISSN 0022-3239; ISSN 1573-2878/e

Summary: Motivated by the work of {\it F. Facchinei} and {\it C. Kanzow} [SIAM J. Optim. 37, 1150-1161 (1999; Zbl 0997.90085)] on regularization methods for the nonlinear complementarity problem and the work of Ravindran and Gowda 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.

MSC 2000:: *90C33 Complementarity problems
47J20 Inequalities involving nonlinear operators

Keywords: variational inequality problems; regularization methods; minimizing sequences

Citations: Zbl 0997.90085

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