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Zbl 1228.49026
Xiao, Yibin; Huang, Nanjing
Well-posedness for a class of variational-hemivariational inequalities with perturbations. (English)
[J] J. Optim. Theory Appl. 151, No. 1, 33-51 (2011). ISSN 0022-3239; ISSN 1573-2878/e

Summary: We consider an extension of well-posedness for a minimization problem to a class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed variational-hemivariational inequality and give some conditions under which the variational-hemivariational inequality is strongly well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the well-posedness of variational-hemivariational inequality and the well-posedness of the corresponding inclusion problem.

MSC 2000:: *49K40 Sensitivity of optimal solutions in the presence of perturbations
49J40 Variational methods including variational inequalities

Keywords: variational-hemivariational inequality; well-posedness; Clarke's generalized gradient; approximating sequence; inclusion problem

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