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.
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This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science.
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Alber, Y.I., Notik, A.I. Perturbed unstable variational inequalities with unbounded operators on approximately given sets. Set-Valued Anal 1, 393–402 (1993). https://doi.org/10.1007/BF01027828
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DOI: https://doi.org/10.1007/BF01027828