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. (C) 2009 Elsevier Ltd. All rights reserved.

Bianchi, M., Kassay, G., Pini, R. (2010). Well-posed equilibrium problems. NONLINEAR ANALYSIS, 72(1), 460-468 [10.1016/j.na.2009.06.081].

Well-posed equilibrium problems

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. (C) 2009 Elsevier Ltd. All rights reserved.
Articolo in rivista - Articolo scientifico
Equilibrium problem; Well-posedness; Approximate solution
English
2010
72
1
460
468
none
Bianchi, M., Kassay, G., Pini, R. (2010). Well-posed equilibrium problems. NONLINEAR ANALYSIS, 72(1), 460-468 [10.1016/j.na.2009.06.081].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/10234
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