Well-posedness for vector equilibrium problems

M. Bianchi (), G. Kassay () and R. Pini ()

Mathematical Methods of Operations Research, 2009, vol. 70, issue 1, 182 pages

Abstract: We introduce and study two notions of well-posedness for vector equilibrium problems in topological vector spaces; they arise from the well-posedness concepts previously introduced by the same authors in the scalar case, and provide an extension of similar definitions for vector optimization problems. The first notion is linked to the behaviour of suitable maximizing sequences, while the second one is defined in terms of Hausdorff convergence of the map of approximate solutions. In this paper we compare them, and, in a concave setting, we give sufficient conditions on the data in order to guarantee well-posedness. Our results extend similar results established for vector optimization problems known in the literature. Copyright Springer-Verlag 2009

Keywords: Well-posedness; Vector equilibrium problems; Approximate solutions; 49K40; 90C31 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s00186-008-0239-4

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