Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities
Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities
复制标题
约束吉洪诺夫正则化的收敛率：预测源条件和变分不等式的等价
DOI：
10.1088/0266-5611/27/8/085001
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发表时间：
2011
期刊：
影响因子：
2.1
通讯作者：
B. Hofmann
中科院分区：
文献类型：
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作者：
Jens Flemming;B. Hofmann
在本文中，我们启发的作用，变分不等式获得收敛速度的Tikhonov正则化的非线性不适定问题的凸性约束下凸罚泛函在Banach空间中。变分不等式能够覆盖解决方案的光滑性和结构的非线性统一的方式，不仅无约束，但正如我们所指出的，也为约束Tikhonov正则化。在这种情况下，我们扩展的概念，投影源条件已经在希尔伯特空间到Banach空间，我们在主要定理，这种投影源条件在某种程度上相当于某些变分不等式。导出的变分不等式立即产生的Bregman距离测量的收敛速度。
In this paper, we enlighten the role of variational inequalities for obtaining convergence rates in Tikhonov regularization of nonlinear ill-posed problems with convex penalty functionals under convexity constraints in Banach spaces. Variational inequalities are able to cover solution smoothness and the structure of nonlinearity in a uniform manner, not only for unconstrained but, as we indicate, also for constrained Tikhonov regularization. In this context, we extend the concept of projected source conditions already known in Hilbert spaces to Banach spaces, and we show in the main theorem that such projected source conditions are to some extent equivalent to certain variational inequalities. The derived variational inequalities immediately yield convergence rates measured by Bregman distances.
影响因子：
--
作者：
Bonesky, Thomas;Kazimierski, Kamil S.;Schuster, Thomas
通讯作者：
Schuster, Thomas