  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.
