Well-posed equilibrium problems

Monica Bianchi, Rita Pini, G. Kassay, R. Pini

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

18 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)460-468
Numero di pagine9
RivistaNONLINEAR ANALYSIS
Volume2010
DOI
Stato di pubblicazionePubblicato - 2010

Keywords

  • approximate solutions
  • equilibrium problems
  • well posedness

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