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Tikhonov regularization methods for variational inequality problems. (English) Zbl 0939.90019
Summary: Motivated by the work of F. Facchinei and 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:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
47J20Inequalities involving nonlinear operators