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Sensitivity analysis of generalized variational inequalities. (English) Zbl 0766.49025
Under various structural assumptions the author studies variational inequalities of the form $U\in {\cal K}\sb \lambda$: $a(u,\lambda,v- u)+b(u,v)-b(u,u)\geq\langle A(u,\lambda),v-u\rangle$ for all $v\in{\cal K}\sb \lambda$. It is shown that the hypotheses imposed on the data imply the existence of a unique solution $u=u(\lambda)$ at least if $\lambda$ is contained in some open subset of the parameter domain. Moreover, the function $u(\lambda)$ is differentiable.

49K40Sensitivity, stability, well-posedness of optimal solutions
Full Text: DOI
[1] Dafermos, S.: Sensitivity analysis in variational inequalities. Math. oper. Res. 13, 421-434 (1988) · Zbl 0674.49007
[2] Dafermos, S.; Nagurney, A.: Sensitivity analysis for the asymmetric network equilibrium problem. Math. programming 28, 174-184 (1984) · Zbl 0535.90038
[3] Fiacco, A. V.: Introduction to sensitivity and stability analysis in nonlinear programming. (1983) · Zbl 0543.90075
[4] Noor, M. Aslam: On a class of variational inequalities. J. math. Anal. appl. 128, 138-155 (1987) · Zbl 0631.49004
[5] Tobin, R. L.: Sensitivity analysis for variational inequalities. J. optim. Theory appl. 48, 191-204 (1986) · Zbl 0557.49004