# American Institute of Mathematical Sciences

October  2009, 5(4): 683-696. doi: 10.3934/jimo.2009.5.683

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

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

Received  April 2008 Revised  February 2009 Published  August 2009

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.
Citation: M. H. Li, S. J. Li, W. Y. Zhang. Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems. Journal of Industrial & Management Optimization, 2009, 5 (4) : 683-696. doi: 10.3934/jimo.2009.5.683
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