  This work proposes a new algorithm for solving the graph-fused lasso (GFL), a
method for parameter estimation that operates under the assumption that the
signal tends to be locally constant over a predefined graph structure. The
proposed method applies the alternating direction method of multipliers (ADMM)
algorithm and is based on the decomposition of the objective function into two
components. While ADMM has been widely used in this problem, existing works
such as network lasso decompose the objective function into the loss function
component and the total variation penalty component. In comparison, this work
proposes to decompose the objective function into two components, where one
component is the loss function plus part of the total variation penalty, and
the other component is the remaining total variation penalty. Compared with the
network lasso algorithm, this method has a smaller computational cost per
iteration and converges faster in most simulations numerically.
