  In this paper, we propose a new efficient method for a sparse Gaussian
graphical model with hidden clustering structures by extending a dual spectral
projected gradient (DSPG) method proposed by Nakagaki et al.~(2020). We
establish the global convergence of the proposed method to an optimal solution,
and we show that the projection onto the feasible region can be solved with a
low computational complexity by the use of the pool-adjacent-violators
algorithm. Numerical experiments on synthesis data and real data demonstrate
the efficiency of the proposed method. The proposed method takes 0.91 seconds
to achieve a similar solution to the direct application of the DSPG method
which takes 4361 seconds.
