We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class
of convex optimization problems. An algorithm of this kind has been proposed
for the $L_1$-penalized regression (lasso) in the literature, but it seems to
have been largely ignored. Indeed, it seems that coordinate-wise algorithms are
not often used in convex optimization. We show that this algorithm is very
competitive with the well-known LARS (or homotopy) procedure in large lasso
problems, and that it can be applied to related methods such as the garotte and
elastic net. It turns out that coordinate-wise descent does not work in the
``fused lasso,'' however, so we derive a generalized algorithm that yields the
solution in much less time that a standard convex optimizer. Finally, we
generalize the procedure to the two-dimensional fused lasso, and demonstrate
its performance on some image smoothing problems.

本文介绍了 “逐一” 坐标下降算法及其在 $ L_1 $- 惩罚回归（套索）、garotte 和弹性网络等相关方法中的应用，证明了该算法可以与广泛应用的 LARS（或同伦）过程竞争，在大规模 lasso 问题中引起了不少关注。但注意到它并不适用于 “融合 Lasso”，所以论文提出了一个广义算法，在比标准的凸优化器运行时间更短的时间内得出了解决方案。最后，将该过程推广到二维融合 Lasso，并展示了其在一些图像平滑问题上的性能。