Many problems in statistics and machine learning can be formulated as an optimization problem of a finite sum of non-smooth convex functions. We propose an algorithm to minimize this type of objective functions based on the idea of alternating linearization. Our algorithm retains the simplicity of contemporary methods without any restrictive assumptions on the smoothness of the loss function. We apply our proposed method to solve two challenging problems: overlapping group Lasso and convex regression with sharp partitions (CRISP). Numerical experiments show that our method is superior to the state-of-the-art algorithms, many of which are based on the accelerated proximal gradient method.

可以将统计和机器学习中的许多问题表述为非光滑凸函数的有限和的优化问题。我们基于交替线性化的思想，提出了一种最小化这类目标函数的算法。我们的算法保留了现代方法的简单性，而对损失函数的平滑度没有任何限制性假设。我们应用我们提出的方法来解决两个具有挑战性的问题：重叠组Lasso和具有尖锐分割的凸回归（CRISP）。数值实验表明，我们的方法优于最新的算法，其中许多算法都是基于加速近端梯度法。