Sensitivity analysis of solutions to a class of quasi-variational inequalities
Adly, Samir ; Ait Mansour, Mohamed ; Scrimali, Laura
Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005), p. 767-771 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality Q⁢V⁢I⁢u∈K⁢u,C⁢u,v-u≥0,∀v∈K⁢u, when both the operator C and the convex K are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).

Si propone un risultato di sensitività delle soluzioni di disequazioni quasi- variazionali finito-dimensionali del tipo: Q⁢V⁢I⁢u∈K⁢u,C⁢u,v-u≥0,∀v∈K⁢u, in presenza di perturbazioni dell'operatore C e dell'insieme convesso K. In particolare, si prova la continuità Hölderiana degli insiemi delle soluzioni dei problemi perturbati intorno al problema iniziale. I risultati illustrati possono essere estesi anche al caso infinito-dimensionale.

Publié le : 2005-10-01
@article{BUMI_2005_8_8B_3_767_0,
     author = {Samir Adly and Mohamed Ait Mansour and Laura Scrimali},
     title = {Sensitivity analysis of solutions to a class of quasi-variational inequalities},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {8-A},
     year = {2005},
     pages = {767-771},
     zbl = {1150.49010},
     mrnumber = {2182428},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_3_767_0}
}

Adly, Samir; Ait Mansour, Mohamed; Scrimali, Laura. Sensitivity analysis of solutions to a class of quasi-variational inequalities. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 767-771. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_3_767_0/

[1] Ait Mansour, M. - Riahi, H., Sensitivity analysis for abstract equilibrium problems, J. Math. Anal. App., 306 No. 2 (2005), 684-691. | MR 2136342 | Zbl 1068.49005

[2] Attouch, H. - Wets, R., Quantitative stability of variational systems: I. The epigraphical distance, Trans. Am. math. Soc., 328 No. 2, (1991), 695-729. | MR 1018570 | Zbl 0753.49007

[3] Aubin, J.-P., Lipschitz behavior of solutions to convex minimization problems, Math. Oper. Res., 9 (1984), 87-111. | MR 736641 | Zbl 0539.90085

[4] Scrimali, L., Quasi-Variational inequalities in Transportation networks, Math. Models. Meth. Appl. Sci, 14, No. 10 (2004), 1541-1560. | MR 2095302 | Zbl 1069.90026

[5] Shapiro, A., Sensitivity analysis of generalized equations, Journal of Mathematical Sciences, 115 (2003), 2554-2565. | MR 1992992 | Zbl 1136.90482

[6] Shapiro, A., Sensitivity analysis of parameterized variational inequalities, Mathematics of Operations Research, 30 (2005), 109-126. | MR 2125140 | Zbl 1082.49015

[7] Walkup, D. W. - J-B. Wets, R., A Lipschitzian of convex polyhedral, Proc. Amer. Math. Society, 23 (1969), 167-178. | MR 246200 | Zbl 0182.25003