Abstract and Applied Analysis

Iterative solution of unstable variational inequalities on approximately given sets

Y. I. Alber, A. G. Kartsatos, and E. Litsyn

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Abstract

The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator A, the “right hand side” f and the set of constraints Ω) are to be perturbed. The connection between the parameters of regularization and perturbations which guarantee strong convergence of approximate solutions is established. In contrast to previous publications by Bruck, Reich and the first author, we do not suppose here that the approximating sequence is a priori bounded. Therefore the present results are new even for operator equations in Hilbert and Banach spaces. Apparently, the iterative processes for problems with perturbed sets of constraints are being considered for the first time.

Article information

Source
Abstr. Appl. Anal., Volume 1, Number 1 (1996), 45-64.

Dates
First available in Project Euclid: 7 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049725991

Digital Object Identifier
doi:10.1155/S1085337596000024

Mathematical Reviews number (MathSciNet)
MR1390559

Zentralblatt MATH identifier
0932.49014

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 65K10
Secondary: 47A55 47H05 65L20

Keywords
Banach spaces variational inequalities convex sets methods of iterative regularization Lyapunov functionals metric projection operators monotone operators perturbations Hausdorff distance convergence stability

Citation

Alber, Y. I.; Kartsatos, A. G.; Litsyn, E. Iterative solution of unstable variational inequalities on approximately given sets. Abstr. Appl. Anal. 1 (1996), no. 1, 45--64. doi:10.1155/S1085337596000024. https://projecteuclid.org/euclid.aaa/1049725991


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References

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