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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 24, Issue 3


Stable gradient projection method for nonlinear conditionally well-posed inverse problems

Mikhali Y. Kokurin
Published Online: 2015-11-17 | DOI: https://doi.org/10.1515/jiip-2015-0047


We study the standard gradient projection method in a Hilbert space, as applied to minimization of the residual functional for nonlinear operator equations with differentiable operators. The functional is minimized over a closed, convex and bounded set, which contains a solution to the equation. It is assumed that the inverse problem associated with the operator equation is conditionally well-posed with a Hölder-type modulus of relative continuity. We prove that the iterative process is asymptotically stable with respect to errors in the right part of the operator equation. Moreover, the process delivers in the limit an order optimal approximation to the desired solution.

Keywords: Ill-posed problem; conditionally well-posed problem; regularizing operator; relatively continuous operator; gradient projection method; convergence; stability

MSC: 65J20; 65J22; 47J06; 47J25

About the article

Received: 2015-05-08

Accepted: 2015-09-15

Published Online: 2015-11-17

Published in Print: 2016-06-01

Funding Source: RFBR

Award identifier / Grant number: 15–07–99514a

The work was partially supported by the RFBR Grant No. 15-07-99514a.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 24, Issue 3, Pages 323–332, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2015-0047.

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