Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience on a variety of problems, namely, multi-period portfolio optimization, classification of data coming from functional Magnetic Resonance Imaging, restoration of images corrupted by Poisson noise, and classification via regularized logistic regression, provides substantial evidence that interior point methods, equipped with suitable linear algebra, can offer a noticeable advantage over first-order approaches.

中文翻译：

---

内点法的稀疏近似

寻求稀疏解决方案的大规模优化问题已无处不在。通常使用各种专门的一阶方法求解它们。尽管这种方法通常很快，但它们通常会遇到条件不太好的问题。在本文中，提出了内点近乘方法的特殊变体，并针对此类问题进行了分析。关于多个问题的计算经验，包括多周期投资组合优化，来自功能磁共振成像的数据分类，受泊松噪声破坏的图像的恢复以及通过正则逻辑回归进行的分类，提供了充分的证据证明内部点方法已配备具有合适的线性代数，可以提供比一阶方法明显的优势。