In this paper, we consider the asymptotical regularization with convex constraints for nonlinear ill-posed problems. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy. Under certain conditions we give convergence properties of the methods. Moreover, we propose Runge-Kutta type methods to discrete the initial value problems to construct new type iterative regularization methods.

翻译：在本文中,我们考虑的是非线性弊病无症状的无症状的正规化,对非线性弊病有相同的限制。该方法允许使用非平稳的处罚条款,包括L1类刑罚和完全变异的处罚功能,这些功能对于重建宽度和片状耐久等解决办法的特殊特征具有重要意义。在某些条件下,我们给出了方法的趋同特性。此外,我们提出龙格-库塔型方法,将最初的值问题分离开来,以构建新型迭代规范方法。