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Well-posed equilibrium problems. (English) Zbl 1180.49028
Summary: We introduce some notions of well-posedness for scalar equilibrium problems in complete metric spaces or in Banach spaces. As equilibrium problem is a common extension of optimization, saddle point and variational inequality problems, our definitions originates from the well-posedness concepts already introduced for these problems.
We give sufficient conditions for two different kinds of well-posedness and show by means of counterexamples that these have no relationship in the general case. However, together with some additional assumptions, we show via Ekeland’s principle for bifunctions a link between them.
Finally we discuss a parametric form of the equilibrium problem and introduce a well-posedness concept for it, which unifies the two different notions of well-posedness introduced in the first part.

MSC:
49K40 Sensitivity, stability, well-posedness
90C31 Sensitivity, stability, parametric optimization
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