Lipschitzian stability of parametric variational inequalities over perturbed polyhedral convex sets

Lipschitzian stability of parametric variational inequalities over perturbed polyhedral convex sets

0.00 Avg rating0 Votes
Article ID: iaor20123495
Volume: 6
Issue: 4
Start Page Number: 749
End Page Number: 762
Publication Date: Apr 2012
Journal: Optimization Letters
Authors:
Keywords: polyhedra, mapping, Lipschitz functions
Abstract:

In this paper we investigate the Lipschitz‐like property of the solution mapping of parametric variational inequalities over perturbed polyhedral convex sets. By establishing some lower and upper estimates for the coderivatives of the solution mapping, among other things, we prove that the solution mapping could not be Lipschitz‐like around points where the positive linear independence condition is invalid. Our analysis is based heavily on the Mordukhovich criterion (Mordukhovich in Variational Analysis and Generalized Differentiation. vol. I: Basic Theory, vol. II: Applications. Springer, Berlin, 2006) of the Lipschitz‐like property for set‐valued mappings between Banach spaces and recent advances in variational analysis. The obtained result complements the corresponding ones of Nam (2010) and Qui (2011).

Reviews

Required fields are marked *. Your email address will not be published.