TY - JOUR
T1 - Well-posed equilibrium problems
AU - Bianchi, Monica
AU - Pini, Rita
AU - Kassay, G.
AU - Pini, R.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
KW - approximate solutions
KW - equilibrium problems
KW - well posedness
KW - approximate solutions
KW - equilibrium problems
KW - well posedness
UR - http://hdl.handle.net/10807/22130
U2 - 10.1016/j.na.2009.06.081
DO - 10.1016/j.na.2009.06.081
M3 - Article
VL - 2010
SP - 460
EP - 468
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
ER -