我们提出了一种有效的谱投影梯度算法，用于优化群L1范数约束。

We present an efficient spectralprojected-gradient algorithm for optimization subject to a group L1-normconstraint.

我们的方法是基于一种创新的线性时间算法，用于L1和群L1范数约束的欧氏投影。

Our approach is based on a novellinear-time algorithm for Euclidean projection onto the L1- and group L1-normconstraints.

在大型数据集上的数值实验表明该方法比现有方法更加有效，并具有可扩展性。

Numerical experiments on large data setssuggest that the proposed method is substantially more efficient and scalablethan existing methods.

稀疏性促进正则化的参数估计是机器学习界非常感兴趣的话题。

Parameter estimation withsparsity-promoting regularization is a topic of substantial interest to themachine learning community.

可能促进参数向量中稀疏性的最成功的方法是L1-正则化，这是广泛使用的最小绝对收缩和选择（Lasso）和基础追踪去噪（BPDN）模型的基石。

Perhaps the most successful approach forpromoting sparsity in the parameter vector is L1-regularization, which is thecornerstone of the widely-used least-absolute shrinkage and selection (Lasso)and basis pursuit denoising (BPDN) models.

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