  We consider the augmented Lagrangian method (ALM) as a solver for the fused
lasso signal approximator (FLSA) problem. The ALM is a dual method in which
squares of the constraint functions are added as penalties to the Lagrangian.
In order to apply this method to FLSA, two types of auxiliary variables are
introduced to transform the original unconstrained minimization problem into a
linearly constrained minimization problem. Each updating in this iterative
algorithm consists of just a simple one-dimensional convex programming problem,
with closed form solution in many cases. While the existing literature mostly
focused on the quadratic loss function, our algorithm can be easily implemented
for general convex loss. The most attractive feature of this algorithm is its
simplicity in implementation compared to other existing fast solvers. We also
provide some convergence analysis of the algorithm. Finally, the method is
illustrated with some simulation datasets.
