Landweber-Kaczmarz method in Banach spaces with inexact inner solvers
Landweber-Kaczmarz method in Banach spaces with inexact inner solvers
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DOI：
10.1088/0266-5611/32/10/104005
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发表时间：
2016-03
期刊：
影响因子：
2.1
通讯作者：
Q. Jin
中科院分区：
文献类型：
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作者：
Q. Jin
近年来，Landweber-Kaczmarz方法被提出来用于求解Banach空间中的非线性不适定反问题。该方法的实现涉及解决一个（非光滑）凸最小化问题在每个迭代步骤和现有的理论需要其精确的决议，在一般情况下是不可能的，在实际应用中。在本文中，我们提出了一个版本的Landweber-Kaczmarz方法在Banach空间中，在每个迭代步骤中所涉及的最小化问题是不精确地解决。基于ε -次微分理论，给出了算法的收敛性分析.此外，使用Nesterov的策略，我们提出了一个可能的加速版本的Landweber-Kaczmarz方法。计算机断层扫描和偏微分方程参数识别的数值结果提供支持我们的理论结果，并证明我们的加速方法。
In recent years the Landweber-Kaczmarz method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization problem at each iteration step and the existing theory requires its exact resolution which in general is impossible in practical applications. In this paper we propose a version of the Landweber-Kaczmarz method in Banach spaces in which the minimization problem involved in each iteration step is solved inexactly. Based on the ε -subdifferential calculus we give a convergence analysis of our method. Furthermore, using Nesterov's strategy, we propose a possible accelerated version of the Landweber-Kaczmarz method. Numerical results on computed tomography and parameter identification in partial differential equations are provided to support our theoretical results and to demonstrate our accelerated method.