论文标题
在Tikhonov功能上受到Bregman距离的惩罚
On Tikhonov functionals penalized by Bregman distances
论文作者
论文摘要
我们研究了在Banach空间中非线性不足问题的Tikhonov正则化方法，在布雷格曼距离描述了罚款。我们证明了收敛性和稳定性结果。此外，使用适当的源条件，我们能够根据布雷格曼距离得出收敛速度。我们还为非线性问题分析了迭代的Tikhonov方法，其中惩罚由适当的凸功能给出。
We investigate Tikhonov regularization methods for nonlinear ill-posed problems in Banach spaces, where the penalty term is described by Bregman distances. We prove convergence and stability results. Moreover, using appropriate source conditions, we are able to derive rates of convergence in terms of Bregman distances. We also analyze an iterated Tikhonov method for nonlinear problems, where the penalization is given by an appropriate convex functional.
