  We consider learning an undirected graphical model from sparse data. While
several efficient algorithms have been proposed for graphical lasso (GL), the
alternating direction method of multipliers (ADMM) is the main approach taken
concerning for joint graphical lasso (JGL). We propose proximal gradient
procedures with and without a backtracking option for the JGL. These procedures
are first-order and relatively simple, and the subproblems are solved
efficiently in closed form. We further show the boundedness for the solution of
the JGL problem and the iterations in the algorithms. The numerical results
indicate that the proposed algorithms can achieve high accuracy and precision,
and their efficiency is competitive with state-of-the-art algorithms.
