×

zbMATH — the first resource for mathematics

Hölder continuity of solutions to a parametric variational inequality. (English) Zbl 0821.49011
The author has investigated a Hölder continuity property of the locally unique solution to a parametric variational inequality without assuming differentiability of the given data. The results proved in this paper represent a refinement of previous results.
Reviewer: M.A.Noor (Riyadh)

MSC:
49J40 Variational inequalities
49K40 Sensitivity, stability, well-posedness
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alt, W. (1983), Lipschitzian perturbations of infinite optimization problems, in: Mathematical Programming with Data Perturbations, II, edited by A. V. Fiacco, Marcel Dekker, New York, pp. 7-21.
[2] Attouch, H., and Wets, R. J.-B. (1992), Quantitative stability of variational systems, II. A framework for nonlinear conditioning, SIAM J. Optim., 3:359-381. · Zbl 0793.49005
[3] Aubin, J.-P. (1984), Lipschitz behavior of solutions to convex minimization problems, Math. Oper. Res., 9:87-111. · Zbl 0539.90085
[4] Clarke, F. H. (1983), Optimization and Nonsmooth Analysis, Wiley Interscience, New York. · Zbl 0582.49001
[5] Dafermos, S. (1988), Sensitivity analysis in variational inequalities, Math. Oper. Res., 13:421-434. · Zbl 0674.49007
[6] Fiacco, A. V. (1983), Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York. · Zbl 0543.90075
[7] Harker, P. T., and Pang, J.-S. (1990), Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms, and applications, Math. Programming, 48:161-220. · Zbl 0734.90098
[8] Kyparisis, J. (1990), Solution differentiability for variational inequalities, Math. Programming, 48:285-301. · Zbl 0727.90082
[9] Mangasafian, O. L., and Shiau, T.-H. (1987), Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems, SIAM J. Control Optim., 25:583-595. · Zbl 0613.90066
[10] Qui, Y., and Magnanti, T. L. (1989), Sensitivity analysis for variational inequalities defined on polyhedral sets, Math. Oper. Res., 14:410-432. · Zbl 0698.90069
[11] Robinson, S. M. (1991), An implicit-function theorem for a class of nonsmooth functions, Math. Oper. Res., 16:292-309. · Zbl 0746.46039
[12] Rockafellar, R. T. (1985), Lipschitzian properties of multifunctions, Nonlinear Anal. TMA, 9:867-885. · Zbl 0573.54011
[13] Shapiro, A. (1987), On differentiability of metric projections in Rn, 1: Boundary case, Proc. Amer. Math. Soc., 99:123-128. · Zbl 0613.41030
[14] Shapiro, A. (1988), Sensitivity analysis of nonlinear programs and differentiability properties of metric projections, SIAM J. Control Optim., 26:628-645. · Zbl 0647.90089
[15] Shapiro, A. (1992), Perturbation analysis of optimization problems in Banach spaces, Numer. Funct. Anal. Optim., 13:97-116. · Zbl 0763.49009
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.