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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:
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49K40 Sensitivity, stability, well-posedness
47H14 Perturbations of nonlinear operators
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[1] GONG, L., Global Stability Result for the Generalized Quasivariational Inequality Problem, Journal of Optimization Theory and Applications, Vol. 70, pp. 365-375, 1991. · Zbl 0737.49010
[2] DAFERMOS, S., Sensitivity Analysis in Variational Inequalities, Mathematics of Operations Research, Vol. 13, pp. 421-434, 1988. · Zbl 0674.49007
[3] HARKER, P. T., and PANG, J. S., Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48, pp. 161-220, 1990. · Zbl 0734.90098
[4] TOBIN, R. L., Sensitivity Analysis for Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 48, pp. 191-204, 1986. · Zbl 0557.49004
[5] SIDDIQI, A. H., ANSARI, Q. H., and KHALIQ, A., On Vector Variational-Like Inequalities, Journal Mathematical Analysis and Applications, Vol. 84, pp. 171-180, 1995. · Zbl 0827.47050
[6] CHEN, G. Y., Existence of Solutions for a Vector Variational Inequality: An Extension of the Hartmann-Stampacchia Theorem, Journal of Optimization Theory and Applications, Vol. 74, pp. 445-456, 1992. · Zbl 0795.49010
[7] CHEN, G. Y., and LI, S. J., Existence of Solutions for a Generalized Vector Quasivariational Inequality, Journal of Optimization Theory and Applications, Vol. 90, pp. 321-334, 1996. · Zbl 0869.49005
[8] DANIILIDIS, A., and HADJISAVVS, N., Existence Theorems for Vector Variational Inequalities, Bulletin of the Australian Mathematical Society, Vol. 54, pp. 473-481, 1996. · Zbl 0887.49004
[9] GIANNESSI, F., Theorems of the Alternative, Quadratic Programs, and Complementary Problems, Variational Inequality and Complementary Problems, Edited by R. W. Cottle, F. Giannessi, and J. C. Lions, John Wiley and Sons, New York, NY, 1980. · Zbl 0484.90081
[10] KONNOV, V., and YAO, J. C., On the Generalized Vector Variational Inequality Problem, Journal of Mathematical Analysis and Applications, Vol. 206, pp. 42-58, 1997. · Zbl 0878.49006
[11] LEE, G. M., KIM, D. S., and LEE, B. S., On Generalized Vector Variational Inequality, Applied Mathematics Letters, Vol. 9, pp. 39-42, 1996. · Zbl 0862.49014
[12] DANIELE, P., and MAUGERI, A., Vector Variational Inequality and Modeling of a Continuum Traffic Equilibrium Problem, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Edited by F. Giannessi, Kluwer Academic Publishers, Doedrecht, Holland, Vol. 38, pp. 97-112, 2000. · Zbl 0967.49008
[13] YANG, X. Q., and GOH, C. J., Vector Variational Inequalities: Application to Vector Equilibria, Journal of Optimization Theory and Applications, Vol. 95, pp. 431-443, 1997. · Zbl 0892.90158
[14] YU, S. J., and YAO, J. C., On Vector Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 89, pp. 749-769, 1996. · Zbl 0848.49012
[15] AUBIN, J. P., and EKELAND, I., Applied Nonlinear Analysis, John Wiley and Sons, New York, NY, 1984. · Zbl 0641.47066
[16] KARAMARDIAN, S., and SCHAIBLE, S., Seven Kinds of Monotone Maps, Journal of Optimization Theory and Applications, Vol. 66, pp. 37-46, 1990. · Zbl 0679.90055
[17] TANINO, T., and SAWARAGI, Y., Stability of Nondominated Solutions in Multicriteria Decision Making, Journal of Optimization Theory and Applications, Vol. 30, pp. 229-253, 1980. · Zbl 0396.90087
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