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Iterative solution of unstable variational inequalities on approximately given sets

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

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.

Suggested Citation

  • Y. I. Alber & A. G. Kartsatos & E. Litsyn, 1996. "Iterative solution of unstable variational inequalities on approximately given sets," Abstract and Applied Analysis, Hindawi, vol. 1, pages 1-20, January.
    • Handle: RePEc:hin:jnlaaa:971253
    DOI: 10.1155/S1085337596000024
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    Cited by:

    1. Mittal, Gaurav & Giri, Ankik Kumar, 2021. "Iteratively regularized Landweber iteration method: Convergence analysis via Hölder stability," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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