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

Robert Plato () and Bernd Hofmann ()
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Robert Plato: University of Siegen
Bernd Hofmann: Chemnitz University of Technology

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 2, No 4, 525-539

Abstract: 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.

Keywords: Nonlinear ill-posed problem; Monotone operator; Variational inequality; Lavrentiev regularization; Adjoint source condition; A priori parameter choice; 49J40; 49K99; 65J15; 65J20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01531-w

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