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. © 2008 Springer-Verlag.

Bianchi, M., Kassay, G., & Pini, R. (2009). Well-posedness for vector equilibrium problems. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 70(1), 171-182 [10.1007/s00186-008-0239-4].

Well-posedness for vector equilibrium problems

PINI, RITA
2009

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. © 2008 Springer-Verlag.
Articolo in rivista - Articolo scientifico
Scientifica
Well--posedness, vector equilibrium problems, approximate solutions
English
171
182
Bianchi, M., Kassay, G., & Pini, R. (2009). Well-posedness for vector equilibrium problems. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 70(1), 171-182 [10.1007/s00186-008-0239-4].
Bianchi, M; Kassay, G; Pini, R
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/8123
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