On Levitin-Polyak \(\alpha\)-well-posedness of perturbed variational-hemivariational inequality. (English) Zbl 1312.49026
Summary: In this paper, we consider an extension of well-posedness for a minimization problem to a class of perturbed Variational-HemiVariational Inequalities with perturbations \((\mathrm{VHVI}_p)\). We establish some metric characterizations for the Levitin-Polyak (LP) \(\alpha\)-well-posedness of \(\mathrm{VHVI}_p\) and give some conditions under which the above problem is LP \(\alpha\)-well-posed in the generalized sense. Links are established between the LP well-posedness of \(\mathrm{VHVI}_p\) and the corresponding inclusion problem.
MSC:
| 49K40 | Sensitivity, stability, well-posedness |
| 49J40 | Variational inequalities |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 90C31 | Sensitivity, stability, parametric optimization |
Keywords:
perturbed variational-hemivariatonal inequalities; Levitin-Polyak \(\alpha\)-well-posedness; approximating sequence; metric characterization; inclusion problemReferences:
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