Well-posed equilibrium problems |
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Authors: | M Bianchi |
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Institution: | a Università Cattolica del Sacro Cuore di Milano, Italy b Babes Bolyai University Cluj, Romania c Università degli Studi di Milano Bicocca, Italy |
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Abstract: | In this paper 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. |
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Keywords: | 49K40 90C31 |
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