A global minimization algorithm for Tikhonov functionals with sparsity constraints
A global minimization algorithm for Tikhonov functionals with sparsity constraints
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DOI：
10.1080/00036811.2014.931025
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发表时间：
2014-01
影响因子：
1.1
通讯作者：
Wei Wang;Stephan W. Anzengruber;R. Ramlau;B. Han
中科院分区：
文献类型：
--
作者：
Wei Wang;Stephan W. Anzengruber;R. Ramlau;B. Han
本文对Banach空间中的非线性正向算子提出了一个计算具有稀疏促进罚项的Tikhonov泛函极小值的全局收敛算法。对偶TIGRA方法在正则化参数的递减值处在对偶空间中使用梯度下降迭代，其中用获得的近似值用作具有参数的对偶迭代的起始值。该方法以偏差原理为全局停止准则，进一步实现了参数的自动选择。在适当的步长选择和停止规则下，我们证明了算法的收敛性，并用非线性自卷积问题的数值实验来说明我们的理论结果。
In this paper, we present a globally convergent algorithm for the computation of a minimizer of the Tikhonov functional with sparsity promoting penalty term for nonlinear forward operators in Banach space. The dual TIGRA method uses a gradient descent iteration in the dual space at decreasing values of the regularization parameter , where the approximation obtained with serves as the starting value for the dual iteration with parameter . With the discrepancy principle as a global stopping rule, the method further yields an automatic parameter choice. We prove convergence of the algorithm under suitable step-size selection and stopping rules and illustrate our theoretic results with numerical experiments for the nonlinear autoconvolution problem.