论文标题
在Banach空间中的换额罚款，差异正规化
Variational regularization with oversmoothing penalty term in Banach spaces
论文作者
论文摘要
在目前的工作中，我们讨论了针对不适合非线性问题的差异正则化，重点是过度平滑的罚款。这意味着在我们的模型中，所考虑的非线性操作员方程的搜索解决方案不属于惩罚功能的定义领域。在过去的几年中，这种变异正则化已在希尔伯特量表中进行了全面研究。我们目前的研究试图继续并将这些调查扩展到Banach量表。这项新研究包括正则化参数的先验选择的收敛速率结果，包括Hölder-Type平滑度和低订单型平滑度。提供了Banach空间设置中低订单平滑度的必要工具。
In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-for solution of the considered nonlinear operator equation does not belong to the domain of definition of the penalty functional. In the past years, such variational regularization has been investigated comprehensively in Hilbert scales. Our present study tries to continue and to extend those investigations to Banach scales. This new study includes convergence rates results for a priori choices of the regularization parameter, both for Hölder-type smoothness and low order-type smoothness. The necessary tools for low order smoothness in the Banach space setting are provided.
