IMRO: A Proximal Quasi-Newton Method for Solving $\ell_1$-Regularized Least Squares Problems
提出一种Hessian近似为“单位矩阵减秩一”的近端拟牛顿方法，有效求解ℓ1正则化最小二乘问题，在压缩感知、机器学习和统计学的稀疏恢复应用中优于现有求解器，并给出了复杂度分析。
We present a proximal quasi-Newton method in which the approximation of the Hessian has the special format of “identity minus rank one” (IMRO) in each iteration. The proposed structure enables us to effectively recover the proximal point. The algorithm is applied to $\ell_1$-regularized least squares problems arising in many applications including sparse recovery in compressive sensing, machine learning, and statistics. Our numerical experiment suggests that the proposed technique competes favorably with other state-of-the-art solvers for this class of problems. We also provide a complexity analysis for variants of IMRO, showing that it matches known best bounds.