A note on Lipschitzian stability of variational inequalities over perturbed polyhedral convex sets

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• 作者：Nguyen Thi Quynh Trang
• 刊名：Optimization Letters
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：10
• 期：6
• 页码：1221-1231
• 全文大小：402 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operation Research and Decision Theory
  Numerical and Computational Methods in Engineering
  Numerical and Computational Methods
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1862-4480
• 卷排序：10

文摘

In the previous paper (Optim lett 6:749–762, 2012), under some technical assumptions, we proved that the solution mapping of variational inequalities over perturbed polyhedral convex sets is not Lipschitz-like around points at which the positively linear dependence of the active vectors defining the constraint set is valid. This note shows that the result holds without such assumptions. In addition, for more deeply understanding the results on the Lipschitz-like stability, some examples have been presented.KeywordsLipschitz-like propertyVariational inequalityPerturbed polyhedral convex set