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On the stability of generalized vector quasivariational inequality problems. (English) Zbl 1003.47049
Summary: We obtain some stability results for generalized vector quasivariational inequality problems. We prove that the solution set is a closed set and establish the upper semicontinuity property of the solution set for perturbed generalized vector quasivariational inequality problems. These results extend those obtained in L. Gong, J. Optimization Theory Appl. 70, No. 2, 365-375 (1991; Zbl 0737.49010). We obtain also the lower semicontinuity property of the solution set for perturbed classical variational inequalities. Several examples are given for the illustration of our results.
MSC:
47J20Inequalities involving nonlinear operators
49K40Sensitivity, stability, well-posedness of optimal solutions
47H14Perturbations of nonlinear operators