Sensitivity analysis of solutions to a class of quasi-variational inequalities

Samir Adly; Mohamed Ait Mansour; Laura Scrimali

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 767-771
  • ISSN: 0392-4033

Abstract

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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).

How to cite

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Adly, Samir, Ait Mansour, Mohamed, and Scrimali, Laura. "Sensitivity analysis of solutions to a class of quasi-variational inequalities." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 767-771. <http://eudml.org/doc/196259>.

@article{Adly2005,
abstract = {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).},
author = {Adly, Samir, Ait Mansour, Mohamed, Scrimali, Laura},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {Hölder continuity; quasi-variational inequalities; perturbations},
language = {eng},
month = {10},
number = {3},
pages = {767-771},
publisher = {Unione Matematica Italiana},
title = {Sensitivity analysis of solutions to a class of quasi-variational inequalities},
url = {http://eudml.org/doc/196259},
volume = {8-B},
year = {2005},
}

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 dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 767
EP - 771
AB - 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).
LA - eng
KW - Hölder continuity; quasi-variational inequalities; perturbations
UR - http://eudml.org/doc/196259
ER -

References

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  1. AIT MANSOUR, M. - RIAHI, H., Sensitivity analysis for abstract equilibrium problems, J. Math. Anal. App., 306 No. 2 (2005), 684-691. Zbl1068.49005MR2136342
  2. ATTOUCH, H. - WETS, R., Quantitative stability of variational systems: I. The epigraphical distance, Trans. Am. math. Soc., 328 No. 2, (1991), 695-729. Zbl0753.49007MR1018570
  3. AUBIN, J.-P., Lipschitz behavior of solutions to convex minimization problems, Math. Oper. Res., 9 (1984), 87-111. Zbl0539.90085MR736641
  4. SCRIMALI, L., Quasi-Variational inequalities in Transportation networks, Math. Models. Meth. Appl. Sci, 14, No. 10 (2004), 1541-1560. Zbl1069.90026MR2095302
  5. SHAPIRO, A., Sensitivity analysis of generalized equations, Journal of Mathematical Sciences, 115 (2003), 2554-2565. Zbl1136.90482MR1992992
  6. SHAPIRO, A., Sensitivity analysis of parameterized variational inequalities, Mathematics of Operations Research, 30 (2005), 109-126. Zbl1082.49015MR2125140
  7. WALKUP, D. W. - J-B. WETS, R., A Lipschitzian of convex polyhedral, Proc. Amer. Math. Society, 23 (1969), 167-178. Zbl0182.25003MR246200

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