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Anh, Lam Quoc; Khanh, Phan Quoc

Semicontinuity of the approximate solution sets of multivalued quasiequilibrium problems. (English) Zbl 1211.90243

Numer. Funct. Anal. Optim. 29, No. 1-2, 24-42 (2008).
The authors study the set of approximate solutions to multivalued quasi-equilibrium problems in a rather general setting. They derive sufficient conditions for lower/upper semicontinuity and Hausdorff lower/upper semicontinuity of these solution sets. Two types of \(\varepsilon\)-solutions are considered. Quasi-variational inequalities, fixed point problems and quasi-optimization problems are discussed as special cases.
Reviewer: Georg Still (Enschede)

Cited in 42 Documents

MSC:

90C31 Sensitivity, stability, parametric optimization
49J53 Set-valued and variational analysis

Keywords:

closedness of multifunctions; \(\varepsilon\)-fixed points; \(\varepsilon\)-quasi-optimization problems; \(\varepsilon\)-solutions; Hausdorff lower and upper semicontinuity; lower and upper semicontinuity; quasi-equilibrium problems; quasi-variational inequalities
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