# American Institute of Mathematical Sciences

July  2015, 11(3): 701-714. doi: 10.3934/jimo.2015.11.701

## Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems

 1 School of Mathematics, Chongqing Normal University, Chongqing 400047, China, China

Received  February 2012 Revised  May 2014 Published  October 2014

In this paper, we introduce two types of Levitin-Polyak well-posedness for a system of generalized vector variational inequality problems. By means of a gap function of the system of generalized vector variational inequality problems, we establish equivalence between the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequality problems and the corresponding well-posednesses of the minimization problems. We also present some metric characterizations for the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequality problems. The results in this paper generalize, extend and improve some known results in the literature.
Citation: Jian-Wen Peng, Xin-Min Yang. Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (3) : 701-714. doi: 10.3934/jimo.2015.11.701
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