Geodesic
Sensitivity analysis of solutions to a class of quasi-variational inequalities
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 767-771.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality $$ (QVI) \qquad u\in K(u), \langle C(u), v-u\rangle \geq0, \qquad \forall v \in K(u), $$ 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: $$ (QVI) \qquad u\in K(u), \langle C(u), v-u\rangle \geq0, \qquad \forall v \in K(u), $$ 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. 
@article{BUMI_2005_8_8B_3_a14,
     author = {Adly, Samir and Ait Mansour, Mohamed and Scrimali, Laura},
     title = {Sensitivity analysis of solutions to a class of quasi-variational inequalities},
     journal = {Bollettino della Unione matematica italiana},
     pages = {767--771},
     publisher = {mathdoc},
     volume = {Ser. 8, 8B},
     number = {3},
     year = {2005},
     zbl = {1150.49010},
     mrnumber = {2136342},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a14/}
}
TY  - JOUR
AU  - Adly, Samir
AU  - Ait Mansour, Mohamed
AU  - Scrimali, Laura
TI  - Sensitivity analysis of solutions to a class of quasi-variational inequalities
JO  - Bollettino della Unione matematica italiana
PY  - 2005
SP  - 767
EP  - 771
VL  - 8B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a14/
LA  - en
ID  - BUMI_2005_8_8B_3_a14
ER  - 
%0 Journal Article
%A Adly, Samir
%A Ait Mansour, Mohamed
%A Scrimali, Laura
%T Sensitivity analysis of solutions to a class of quasi-variational inequalities
%J Bollettino della Unione matematica italiana
%D 2005
%P 767-771
%V 8B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a14/
%G en
%F BUMI_2005_8_8B_3_a14
Adly, Samir; Ait Mansour, Mohamed; Scrimali, Laura. Sensitivity analysis of solutions to a class of quasi-variational inequalities. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 767-771. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a14/

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

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

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

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

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

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

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