SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1415-1445, January 2020.
As second-order methods, Gauss--Newton-type methods can be more effective than first-order methods for the solution of nonsmooth optimization problems with expensive-to-evaluate smooth components. Such methods, however, often do not converge. Motivated by nonlinear inverse problems with nonsmooth regularization, we propose a new Gauss--Newton-type method with inexact relaxed steps. We prove that the method converges to a set of disjoint critical points given that the linearization of the forward operator for the inverse problem is sufficiently precise. We extensively evaluate the performance of the method on electrical impedance tomography (EIT).

中文翻译：

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高斯弛豫-牛顿法及其在电阻抗层析成像中的应用

SIAM影像科学杂志，第13卷，第3期，第1415-1445页，2020年1月。
作为二阶方法，高斯-牛顿型方法比一阶方法更有效地解决了非光滑优化问题。评估平滑组件的成本很高。但是，这些方法通常不会收敛。基于非光滑正则化的非线性逆问题，我们提出了一种新的具有不精确松弛步长的高斯-牛顿型方法。我们证明了该方法收敛到一组不相交的临界点，因为反问题的正向算子的线性化足够精确。我们广泛评估了该方法在电阻抗断层扫描（EIT）方面的性能。