# American Institute of Mathematical Sciences

2011, 1(2): 317-331. doi: 10.3934/naco.2011.1.317

## Stability analysis of parametric variational systems

 1 College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China, China

Received  October 2010 Revised  May 2011 Published  June 2011

In this paper, Robinson's metric regularity of a positive order around/at some point of parametric variational systems is discussed. Under some suitable conditions, the relationships among H$\ddot{o}$lder-likeness, H$\ddot{o}$lder calmness, metric regularity of a positive order and Robinson's metric regularity of a positive order are discussed for the parametric variational systems. Then, some applications to the stabilities of the optimal value map and the solution map are studied for a parametric vector optimization problem, respectively.
Citation: Shengji Li, Chunmei Liao, Minghua Li. Stability analysis of parametric variational systems. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 317-331. doi: 10.3934/naco.2011.1.317
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