ISSN:
1572-932X
Keywords:
Primary: 49J40, 65K10, 47A55, 47H05, 65L20
;
Variational inequality
;
perturbation
;
unbounded and nonsmooth operators
;
convex sets
;
Hausdorff distance
;
regularization
;
monotonicity
;
convergence
;
stability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains Ω are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01027828
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