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.

翻译：寻求稀少解决办法的大规模优化问题已变得无处不在,通常通过各种专门的第一阶方法加以解决,虽然这些方法往往速度很快,但通常会遇到条件不完善的问题;在本文件中,针对这一类问题,提出并分析内部点准乘数方法的专门变体。 关于各种问题的计算经验,即多期组合优化、功能性磁共振成像数据分类、恢复被Poisson噪音腐蚀的图像以及通过正规化后勤回归进行分类,这些都提供了大量证据,证明配备适当线性代数的内点方法能够提供明显优势,而不是一阶方法。