A semismooth Newton method for Tikhonov functionals with sparsity constraints
A semismooth Newton method for Tikhonov functionals with sparsity constraints
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DOI：
10.1088/0266-5611/24/3/035007
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发表时间：
2007-09
期刊：
影响因子：
2.1
通讯作者：
R. Griesse;Dirk A. Lorenz
中科院分区：
文献类型：
--
作者：
R. Griesse;Dirk A. Lorenz
研究了具有稀疏约束的Tikhonov泛函在ℓ2中的极小化问题。解的稀疏性通过加权的ℓ1惩罚项来保证。证明了最优性的充要条件是斜可微的(牛顿可微)，因此半光滑牛顿法是可行的。证明了该方法的局部超线性收敛。数值算例表明，与已有方法相比，该方法具有更好的性能。
Minimization problems in ℓ2 for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted ℓ1 penalty term. The necessary and sufficient condition for optimality is shown to be slantly differentiable (Newton differentiable), hence a semismooth Newton method is applicable. Local superlinear convergence of this method is proved. Numerical examples are provided which show that our method compares favorably with existing approaches.