×

Sensitivity analysis for a new system of generalized nonlinear mixed quasi-variational inclusions. (English) Zbl 1056.49008

Summary: We introduce a new system of generalized nonlinear mixed quasi-variational inclusions, prove the existence of solutions, and give the sensitivity analysis of solutions in Hilbert spaces.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49K40 Sensitivity, stability, well-posedness
90C31 Sensitivity, stability, parametric optimization
Full Text: DOI

References:

[1] Agarwal, R. P.; Cho, Y. J.; Huang, N. J., Sensitivity analysis for strongly nonlinear quasi-variational inclusions, Appl. Math. Lett., 13, 6, 19-24 (2000) · Zbl 0960.47035
[2] Baiocchi, C.; Caopelo, A., Variational and Quasivariational Inequalities, Application to Free Boundary Problems (1984), Wiley: Wiley New York · Zbl 0551.49007
[3] Bensounssan, A.; Lions, J. L., Impulse Control and Quasivariational Inequalities (1984), Gauthiers-Villers: Gauthiers-Villers Bordas
[4] Harker, P. T.; Pang, J. S., Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithm and application, Math. Programming, 48, 161-220 (1990) · Zbl 0734.90098
[5] Huang, N. J., Generalized nonlinear implicit quasivariational inclusion and an application to implicit variational inequalities, Z. Angew. Math. Mech., 79, 8, 569-575 (1999) · Zbl 0942.47034
[6] Huang, N. J., Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions, Computers Math. Applic., 35, 10, 1-7 (1998) · Zbl 0999.47057
[7] Huang, N. J.; Bai, M. R.; Cho, Y. J.; Kang, S. M., Generalized nonlinear mixed quasi-variational inequalities, Computers Math. Applic., 40, 2/3, 205-215 (2000) · Zbl 0960.47036
[8] Huang, N. J.; Deng, C. X., Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities, J. Math. Anal. Appl., 256, 345-359 (2001) · Zbl 0972.49008
[9] Verma, R. U., Nonlinear variational and constrained hemivariational inequalities involving relaxed operators, Z. Angew. Math. Mech., 77, 5, 387-391 (1997) · Zbl 0886.49006
[10] Verma, R. U., Iterative algorithm and a new system nonlinear quasivariational inequalities, Adv. Nonlinear Var. Inequal., 4, 1, 117-124 (2001) · Zbl 1014.47050
[11] Verma, R. U., Projection methods, algorithms, and a new system of nonlinear variational inequalities, Computers Math. Applic., 41, 7/8, 1025-1031 (2001) · Zbl 0995.47042
[12] Yuan, G. X.Z, KKM Theory and Applications (1999), Marcel Dekker: Marcel Dekker New York · Zbl 0936.47034
[13] Dafermos, S., Sensitivity analysis in variational inequalities, Math. Oper. Res., 13, 421-434 (1988) · Zbl 0674.49007
[14] Mukherjee, R. N.; Verma, H. L., Sensitivity analysis of generalized variational inequalities, J. Math. Anal. Appl., 167, 299-304 (1992) · Zbl 0766.49025
[15] Noor, M. A., Sensitivity analysis for quasi-variational inequalities, J. Optim. Theory Appl., 95, 399-407 (1997) · Zbl 0896.49003
[16] Yen, N. D., Lipschitz continuity of solution variational inequalities with a parametric polyhedral constraint, Math. Oper. Res., 20, 695-708 (1995) · Zbl 0845.90116
[17] Robinson, S. M., Sensitivity analysis for variational inequalities by normal-map technique, (Giannessi, F.; Maugeri, A., Variational Inequalities and Network Equilibrium Problems (1995), Plenum Press: Plenum Press New York)
[18] Noor, M. A.; Noor, K. I., Sensitivity analysis for quasi-variational inclusions, J. Math. Anal. Appl., 236, 290-299 (1999) · Zbl 0949.49007
[19] Brezis, H., Operateurs Maximaux Monotone et Semigroups de Contractions dans les Espaces de Hilbert (1973), North-Holland: North-Holland Amsterdam · Zbl 0252.47055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.