Stability analysis of parametric variational systems

Shengji Li; Chunmei Liao; Minghua Li

doi:10.3934/naco.2011.1.317

Article Contents

2011, Volume 1, Issue 2: 317-331. Doi: 10.3934/naco.2011.1.317

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Stability analysis of parametric variational systems

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

Received: October 2010

Revised: May 2011

Published: May 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 49J53, 90C31, 49K40; Secondary: 90C29.

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