标题： 在计算统计学中关键问题的稀疏通用求解器 显示英文标题

标题： On computing sparse universal solvers for key problems in statistics

摘要： 我们给出稀疏性结果，并提出算法用于计算与最小二乘问题相关的最小（向量）1-范数通用解算器。特别是，除了通用最小二乘解算器外，我们还考虑最小秩通用最小二乘解算器，以及同时的通用最小范数/最小二乘解算器。对于所有这些情况，我们提出了几种新的替代线性优化公式和非常有效的邻近点算法。总体而言，我们发现这些问题的新 Douglas-Rachford 分裂算法表现最佳。 显示英文摘要

摘要： We give sparsity results and present algorithms for calculating minimum (vector) 1-norm universal solvers connected to least-squares problems. In particular, besides universal least-squares solvers, we consider minimum-rank universal least-squares solvers, and simultaneous universal minimum-norm/least-squares solvers. For all of these, we present and compare several new alternative linear-optimization formulations and very effective proximal-point algorithms. Overall, we found that our new Douglas-Rachford splitting algorithms for these problems performed best.