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Convergence of the gradient method for ill-posed problems

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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.

    Mathematics Subject Classification: Primary: 65J20, 65J15; Secondary: 47J06.


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