On the Convergence of Stochastic Gradient Descent for Nonlinear Ill-Posed Problems
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AbstractIn this work, we analyze the regularizing property of the stochastic gradient descent for the numerical solution of a class of nonlinear ill-posed inverse problems in Hilbert spaces. At each step of the iteration, the method randomly chooses one equation from the nonlinear system to obtain an unbiased stochastic estimate of the gradient and then performs a descent step with the estimated gradient. It is a randomized version of the classical Landweber method for nonlinear inverse problems, and it is highly scalable to the problem size and holds significant potential for solving large-scale inverse problems. Under the canonical tangential cone condition, we prove the regularizing property for a priori stopping rules and then establish the convergence rates under a suitable sourcewise condition and a range invariance condition.
Acceptance Date28/02/2020
All Author(s) ListBangti Jin, Zehui Zhou, Jun Zou
Journal nameSIAM Journal on Optimization
Volume Number30
Issue Number2
PublisherSociety for Industrial and Applied Mathematics
Pages1421 - 1450
LanguagesEnglish-United States
Keywordsstochastic gradient descent, regularizing property, nonlinear inverse problems, convergence rates

Last updated on 2021-13-10 at 23:56