论文标题
放松的高斯 - 牛顿方法，适用于电阻抗断层扫描
Relaxed Gauss-Newton methods with applications to electrical impedance tomography
论文作者
论文摘要
作为二阶方法，Gauss-Newton-type方法比一阶方法更有效，用于解决非平滑优化问题，并具有昂贵的对光滑的光滑组件。但是，这种方法通常不会收敛。由非平滑正规化的非线性反问题激励，我们提出了一种新的高斯 - 牛顿型方法，并具有不精确的步骤。我们证明该方法会收敛到一组不相交的临界点，因为逆问题的远期操作员的线性化足够精确。我们广泛评估了该方法在电阻抗断层扫描（EIT）方面的性能。
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 linearisation of the forward operator for the inverse problem is sufficiently precise. We extensively evaluate the performance of the method on electrical impedance tomography (EIT).
