Iterative Solution of Unstable Variational Inequalities on Approximately Given Sets

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

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

The onvergence 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.

Original languageEnglish
Pages (from-to)45-64
Number of pages20
JournalAbstract and Applied Analysis
Volume1
Issue number1
DOIs
StatePublished - 1 Jan 1996
Externally publishedYes

Keywords

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

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