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.

Bianchi, M., Kassay, G., Pini, R., Well-posed equilibrium problems, <<NONLINEAR ANALYSIS>>, 2010; 2010 (72): 460-468. [doi:10.1016/j.na.2009.06.081] [http://hdl.handle.net/10807/22130]

Well-posed equilibrium problems

Bianchi, Monica;Pini, Rita
2010

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.
Inglese
Bianchi, M., Kassay, G., Pini, R., Well-posed equilibrium problems, <<NONLINEAR ANALYSIS>>, 2010; 2010 (72): 460-468. [doi:10.1016/j.na.2009.06.081] [http://hdl.handle.net/10807/22130]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/22130
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