Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 1, Number 1 (1996), 45-64.
Iterative solution of unstable variational inequalities on approximately given sets
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 , the “right hand side” and the set of constraints ) 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.
Abstr. Appl. Anal., Volume 1, Number 1 (1996), 45-64.
First available in Project Euclid: 7 April 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 65K10
Secondary: 47A55 47H05 65L20
Banach spaces variational inequalities convex sets methods of iterative regularization Lyapunov functionals metric projection operators monotone operators perturbations Hausdorff distance convergence stability
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