Convergence of the gradient method for ill-posed problems

2016/06/01 by Kindermann, Stefan · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1606.00274

Abstract

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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