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

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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.

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Acknowledgements

The authors are grateful for suggestions of two referees, which led to a significantly improved presentation. Research is supported by the German Research Foundation (DFG) under grant HO 1454/12-1.

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Authors and Affiliations

  1. Department of Mathematics, University of Siegen, Walter-Flex-Str. 3, 57068, Siegen, Germany

    Robert Plato

  2. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Bernd Hofmann

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  1. Robert Plato
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  2. Bernd Hofmann
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Correspondence to Robert Plato.

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Asen L. Dontchev.

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Plato, R., Hofmann, B. A Regularized Variational Inequality Approach for Nonlinear Monotone Ill-Posed Equations. J Optim Theory Appl 182, 525–539 (2019). https://doi.org/10.1007/s10957-019-01531-w

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  • DOI: https://doi.org/10.1007/s10957-019-01531-w

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