Levitin-Polyak well-posedness of generalizedvector quasi-equilibrium problems

M. H. Li; S. J. Li; W. Y. Zhang

doi:10.3934/jimo.2009.5.683

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2009, Volume 5, Issue 4: 683-696. Doi: 10.3934/jimo.2009.5.683

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Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems

1.
College of Mathematics and Science, Chongqing University, Chongqing, 400044

Received: March 31, 2008

Revised: January 31, 2009

Published: September 2009

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Abstract

In this paper, Levitin-Polyak well-posedness for two classes of generalized vector quasi-equilibrium problems is introduced. Criteria and characterizations of the Levitin-Polyak well-posedness are investigated. By virtue of gap functions for the generalized vector quasi-equilibrium problems, some equivalent relations are obtained between the Levitin-Polyak well-posedness for optimization problems and the Levitin-Polyak well-posedness for generalized vector quasi-equilibrium problems. Finally, a set-valued version of Ekeland's variational principle is derived and applied to establish a sufficient condition for Levitin-Polyak well-posedness of a class of generalized vector quasi-equilibrium problems.

Keywords:

Levitin-Polyak well-posedness,
generalized vector quasi-equilibrium problems,
approximating solution sequence,
gap function,
Ekeland's variational principle.

Mathematics Subject Classification: 90C31, 49J53.

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