American Institute of Mathematical Sciences

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

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

M. H. Li 1, , S. J. Li 1, and  W. Y. Zhang 1,

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.
Keywords: Ekeland's variational principle., generalized vector quasi-equilibrium problems, approximating solution sequence, Levitin-Polyak well-posedness, gap function.
Mathematics Subject Classification: 90C31, 49J5.
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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