标题： ProPPA：一种用于$\ell_1$最小化和低秩矩阵补全的快速算法 显示英文标题

标题： ProPPA: A Fast Algorithm for $\ell_1$ Minimization and Low-Rank Matrix Completion

摘要： 我们提出了一种投影邻近点算法（ProPPA）来解决一类优化问题。 该算法迭代地计算最后估计解在仿射空间中的邻近点，该仿射空间本身与可行集平行并逐渐接近可行集。 我们从理论上提供了收敛性分析以支持该通用算法，然后将其应用于求解$\ell_1$-最小化问题和矩阵补全问题。 这些问题出现在许多应用中，包括机器学习、图像和信号处理。 我们将我们的算法与现有的最先进算法进行了比较。 在求解这些问题的实验结果表明，我们的算法非常高效且具有竞争力。 显示英文摘要

摘要： We propose a Projected Proximal Point Algorithm (ProPPA) for solving a class of optimization problems. The algorithm iteratively computes the proximal point of the last estimated solution projected into an affine space which itself is parallel and approaching to the feasible set. We provide convergence analysis theoretically supporting the general algorithm, and then apply it for solving $\ell_1$-minimization problems and the matrix completion problem. These problems arise in many applications including machine learning, image and signal processing. We compare our algorithm with the existing state-of-the-art algorithms. Experimental results on solving these problems show that our algorithm is very efficient and competitive.