Abstract In this work, we propose a two-point Landweber-type method with general convex penalty terms for solving nonsmooth nonlinear inverse problems. The design of our method can cope with nonsmooth nonlinear inverse problems or the nonlinear inverse problems whose data are contaminated by various types of noise. The method consists of the two-point acceleration strategy and inner solvers. Inner solvers are used to solve the minimization problems with respect to the penalty terms in each steps. If the minimization problems can be solved explicitly, the inner solvers will be chosen to be the exact solvers. Otherwise, we will use inexact solvers as inner solvers. Convergence results are given without utilizing the Gâteaux differentiability of the forward operator or the reflexivity of the image space. Numerical simulations are given to test the performance of the proposed method.

中文翻译：

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具有凸惩罚项的非光滑非线性逆问题的两点 Landweber 型方法

摘要 在这项工作中，我们提出了一种具有一般凸惩罚项的两点 Landweber 型方法，用于求解非光滑非线性逆问题。我们的方法设计可以处理非光滑非线性逆问题或数据被各种噪声污染的非线性逆问题。该方法由两点加速策略和内部求解器组成。内部求解器用于解决每个步骤中关于惩罚项的最小化问题。如果可以显式解决最小化问题，则将选择内部求解器作为精确求解器。否则，我们将使用不精确求解器作为内部求解器。在没有利用前向算子的 Gâteaux 可微性或图像空间的自反性的情况下给出了收敛结果。