×

zbMATH — the first resource for mathematics

On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems. (English) Zbl 1104.90041
Summary: We consider parametric multivalued vector equilibrium problems of both weak and strong types in metric linear spaces. Sufficient conditions for the local uniqueness and Hölder continuity of the solutions are established. As consequences some new results for variational inequalities are derived and compared with recent papers on the subject.

MSC:
90C27 Combinatorial optimization
91A40 Other game-theoretic models
90C31 Sensitivity, stability, parametric optimization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agarwal, R.P.; Huang, N.J.; Tan, M.Y., Sensitivity analysis for a new system of generalized nonlinear mixed quasivariational inclusions, Appl. math. lett., 17, 345-352, (2004) · Zbl 1056.49008
[2] Anh, L.Q.; Khanh, P.Q., Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems, J. math. anal. appl., 294, 699-711, (2004) · Zbl 1048.49004
[3] L.Q. Anh, P.Q. Khanh, On the stability of the solution sets of general multivalued vector quasiequilibrium problems, submitted for publication · Zbl 1146.90516
[4] Bianchi, M.; Pini, R., A note on stability for parametric equilibrium problems, Oper. res. lett., 31, 445-450, (2003) · Zbl 1112.90082
[5] Dafermos, S., Sensitivity analysis in variational inequalities, Math. oper. res., 13, 421-434, (1988) · Zbl 0674.49007
[6] Ding, X.P., Sensitivity analysis for generalized nonlinear implicit quasivariational inclusions, Appl. math. lett., 17, 225-235, (2004) · Zbl 1056.49010
[7] Harker, P.T.; Pang, J.S., Finite dimensional variational inequalities and nonlinear complementarity problems: A survey of theory, algorithms and applications, Math. program., 48, 161-220, (1990) · Zbl 0734.90098
[8] Mukherjee, R.N.; Verma, H.L., Sensitivity analysis of generalized variational inequalities, J. math. anal. appl., 167, 299-304, (1992) · Zbl 0766.49025
[9] Muu, L.D., Stability property of a class of variational inequalities, Math. operationsforsch. statist. ser. optim., 15, 347-351, (1984) · Zbl 0553.49007
[10] Yen, N.D., Hölder continuity of solutions to parametric variational inequalities, Appl. math. optim., 31, 245-255, (1995) · Zbl 0821.49011
[11] Yen, N.D.; Lee, G.M., Solution sensitivity of a class of variational inequalities, J. math. anal. appl., 215, 48-55, (1997) · Zbl 0906.49002
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.