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Convergence of the gradient method for ill-posed problems

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arxiv 1606.00274 v1 pith:5Z4MGHT5 submitted 2016-06-01 math.NA cs.NA

Stefan Kindermann This is my paper · ORCID
classification math.NAcs.NA
keywords convergencegradientmethodclassicalconditionsfunctionalill-posedproblems
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We study the convergence of the gradient descent method for solving ill-posed problems where the solution is characterized as a global minimum of a differentiable functional in a Hilbert space. The classical least-squares functional for nonlinear operator equations is a special instance of this framework and the gradient method then reduces to Landweber iteration. The main result of this article is a proof of weak and strong convergence under new nonlinearity conditions that generalize the classical tangential cone conditions.

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  1. The tangential cone condition for some coefficient identification model problems in parabolic PDEs

    math.AP 2019-08 accept novelty 6.0 of 10

    The tangential cone condition is verified for potential, diffusion, and nonlinear source identification in parabolic PDEs, establishing convergence of Landweber-type methods in suitable function spaces.

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