We present an Alternating Direction Method of Multipliers (ADMM) algorithm designed to solve the Weighted Generalized Fused LASSO Signal Approximator (wFLSA). First, we show that wFLSAs can always be reformulated as a Generalized LASSO problem. With the availability of algorithms tailored to the Generalized LASSO, the issue appears to be, in principle, resolved. However, the computational complexity of these algorithms is high, with a time complexity of $O(p^4)$ for a single iteration, where $p$ represents the number of coefficients. To overcome this limitation, we propose an ADMM algorithm specifically tailored for wFLSA-equivalent problems, significantly reducing the complexity to $O(p^2)$. Our algorithm is publicly accessible through the R package wflsa.

翻译：本文提出了一种用于求解加权广义融合LASSO信号逼近器（wFLSA）的交替方向乘子法（ADMM）算法。首先，我们证明wFLSA问题总可重构为广义LASSO问题。尽管已有针对广义LASSO设计的算法，该问题在理论上似乎已获解决，但此类算法的计算复杂度较高，单次迭代的时间复杂度达$O(p^4)$（其中$p$表示系数数量）。为突破此限制，我们提出一种专门针对wFLSA等价问题设计的ADMM算法，将复杂度显著降低至$O(p^2)$。本算法已通过R软件包wflsa公开提供。