In this work, we formulate a projected Bouligand–Landweber iteration for non-smooth ill-posed problems. The approach is a combination of Bouligand–Landweber iteration and the projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. Since the forward mapping is not Frchet differentiable, the convergence analysis will be based on the concept of asymptotic stability and a generalized tangential cone condition. Finally, numerical examples will be presented.

中文翻译：

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非光滑不适定问题的预计Bouligand–Landweber迭代

在这项工作中，我们为非光滑不适定问题制定了一个预计的Bouligand-Landweber迭代。该方法结合了Bouligand–Landweber迭代和在条纹上的投影，该条纹的宽度受噪声水平和操作员结构的控制。由于前向映射不是Frchet可微的，因此收敛性分析将基于渐近稳定性和广义切向锥条件的概念。最后，将给出数值示例。