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A Regularized Variational Inequality Approach for Nonlinear Monotone Ill-Posed Equations

Author

Listed:
  • Robert Plato

    (University of Siegen)

  • Bernd Hofmann

    (Chemnitz University of Technology)

Abstract

We consider a regularized variational inequality approach for the stable solution of nonlinear ill-posed problems, where the involved operators are monotone on a given closed, convex subset of a Hilbert space. For suitable a priori parameter choices, we present new error estimates for the subclass of cocoercive operators, provided that the solution admits an adjoint source representation. Some numerical experiments are included.

Suggested Citation

  • Robert Plato & Bernd Hofmann, 2019. "A Regularized Variational Inequality Approach for Nonlinear Monotone Ill-Posed Equations," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 525-539, August.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-019-01531-w
    DOI: 10.1007/s10957-019-01531-w
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