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Zbl 1112.90082
Bianchi, Monica; Pini, Rita
A note on stability for parametric equilibrium problems. (English)
[J] Oper. Res. Lett. 31, No. 6, 445-450 (2003). ISSN 0167-6377

The authors study the stability of perturbed equilibrium problems in vector metric spaces where the function $f$ and the set $K$ are perturbed by the parameters ${\epsilon},\eta$. They study the stability of the solutions, providing some results in the peculiar framework of generalized monotone functions, first in the particular case where $K$ is fixed, then under both data perturbation. It is well known that equilibrium problems include variational inequalities as special case. The references are not up to date. Equilibrium problems considered in this paper were introduced and studied by {\it E. Blum} and {\it W. Oettli} [ Math. Stud. 63, 123--145 (1994; Zbl 0888.49007)] and {\it M. Aslam Noor} and {\it W. Oettli} [Mathematiche 49, 313--331 (1994; Zbl 0839.90124)]. For senstivity analysis of variational inclusions, see, for example, {\it M. A. Noor} [Comput. Math. Appl. 44, 1175--1181 (2002; Zbl 1034.49007)] and references therein.
[Muhammad Aslam Noor (Islamabad)]

MSC 2000:: *90C31 Sensitivity, etc.
49K40 Sensitivity of optimal solutions in the presence of perturbations
90C47 Minimax problems
47N10 Appl. of operator theory in optimization, math. programming, etc.

Keywords: equilibrium problems; sensitivity analysis; variational inequalities

Citations: Zbl 0888.49007; Zbl 0839.90124; Zbl 1034.49007

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