Stochastic variance reduced gradient method for linear ill-posed inverse problems

Qinian Jin; Liuhong Chen

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arXiv · 2403.12460

Stochastic variance reduced gradient method for linear ill-posed inverse problems

Qinian Jin·Liuhong Chen

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Abstract

In this paper we apply the stochastic variance reduced gradient (SVRG) method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in Hilbert spaces. Under {\it a priori} choices of stopping indices, we derive a convergence rate result when the sought solution satisfies a benchmark source condition and establish a convergence result without using any source condition. To terminate the method in an {\it a posteriori} manner, we consider the discrepancy principle and show that it terminates the method in finite many iteration steps almost surely. Various numerical results are reported to test the performance of the method.

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Qinian Jin, Liuhong Chen. 2024-03-19. Stochastic variance reduced gradient method for linear ill-posed inverse problems. https://arxiv.org/abs/2403.12460

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