In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matrix division in the former case, while an efficient method such as FISTA (fast iterative shrinkage-thresholding algorithm) has been developed in the latter case. This paper proposes a general method for converting the ADMM solution to the proximal gradient method, assuming that assumption that the derivative of the objective function is Lipschitz continuous. Then, we apply it to sparse estimation problems, such as sparse convex clustering and trend filtering, and we show by numerical experiments that we can obtain a significant improvement in terms of efficiency.

翻译：在少许估计中,例如结合拉索和混凝土组群,我们要么采用近似梯度法,要么采用乘数交替方向法(ADMM)来解决问题。在前一种情况中,需要时间将矩阵划分包括在内,而在后一种情况中,已经开发出一种有效的方法,如FISTA(快速迭代缩影-超速算法),本文提出了一种将ADMM办法转换为近似梯度法的一般方法,假设目标函数的衍生物是连续的。然后,我们将其应用于稀少的估计问题,如稀少的 convex集群和趋势过滤,我们通过数字实验表明,我们可以大大提高效率。